The point equidistant from the three sides of a triangle is (c) Incenter .
The Circumcenter of a triangle is defined as a point where perpendicular bisectors of sides of triangle intersect. It is also equidistant from 3 vertices of triangle .
The Centroid is defined as a point where 3 medians of the triangle intersect.
The Incenter is defined as a point where angle bisectors of the triangle intersect. It is equidistant from the three sides of the triangle, and is the center of the inscribed circle of the triangle .
The Orthocenter is defined as a point where the 3 altitudes of the triangle intersect.
So , by the definition of the Incenter , the correct option is (c) Incenter .
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The given question is incomplete , the complete question is
The point equidistant from the three sides of a triangle is
(a) Circumcenter
(b) Centroid
(c) Incenter
(d) Orthocenter
There are 4 grams of sugar in 1/2 of a liter of a new sports drink. How much sugar is in 3⁄4 of a liter of the sports drink?
There are 6 grams of sugar in 3/4 of a liter of the sports drink. when There are 4 grams of sugar in 1/2 of a liter of a new sports drink.
To find out how much sugar is in 3/4 of a liter of the sports drink, we need to first calculate the total amount of sugar in 1 liter of the drink. Since there are 4 grams of sugar in 1/2 of a liter, then in 1 liter, there would be 4 x 2 = 8 grams of sugar.
Now that we know there are 8 grams of sugar in 1 liter, we can calculate how much sugar there is in 3/4 of a liter: 8 x (3/4) = 6 grams.
Therefore, there are 6 grams of sugar in 3/4 of a liter of the sports drink.
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Too tired to do it. please answer it for me
A diamond has eight equilateral triangles as faces, as shown. The formula V = 0.4783
approximates the volume (in cubic millimeters) of the diamond, where s is the side length (in millimeters) of each edge. Approximate the length of each edge of the diamond.
V = 161 mm³
The length of each edge of the diamond is about
1
mm.
In equilateral triangles, 7.0 mm is the length of each edge of the diamond.
The equilateral triangle's definition?
An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.
A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.
V = 0.4783 S³ = 161
S³ = 161/0.47
= ∛ 161/0.47
≈ 7.0 mm
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x+1/x+4=3 find the value of x
PLEASE GIVE BRAINLIEST!
thank you and have a good day ;)
Answer:
-11/2
Step-by-step explanation:
Multiply both sides by a polynomial to clear functions
x + 1 = 3(x +4)
x + 1 = 3x + 12
x - 3x = 12 -1
-2x = 11
x = -11/2
I hope this helps
Answer:
The answer can be written in multiple forms
Fraction Form: [tex]x=-\frac{11}{2}[/tex]
Decimal Form: [tex]x=-5.5[/tex]
Step-by-step explanation:
Given
[tex]\frac{x+1}{x+4}=3[/tex]
Lets solve for [tex]x[/tex].
Eliminate the fraction by multiplying each side of the equation by [tex]x+4[/tex].
[tex]x+1=3(x+4)[/tex]
Simplify the right side by applying the distributive property.
[tex]x+1=(3*x)+(3*4)[/tex]
[tex]x+1=3x+12[/tex]
Subtract [tex]3x[/tex] from both sides of the equation.
[tex]x+1-3x=12[/tex]
Add [tex]x[/tex] and [tex]-3x[/tex].
[tex]-2x+1=12[/tex]
Subtract [tex]1[/tex] from both sides of the equation.
[tex]-2x=11[/tex]
Divide each side of the equation by [tex]-2[/tex].
[tex]x=-\frac{11}{2}[/tex]
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The function
y
=
f
(
x
)
y=f(x) is graphed below. Plot a line segment connecting the points on
f
f where
x
=
−
4
x=−4 and
x
=
1.
x=1. Use the line segment to determine the average rate of change of the function
f
(
x
)
f(x) on the interval
−
4
≤
x
≤
1.
−4≤x≤1.
The average rate of change of the function is 1.6
How to to determine the average rate of change of the functionFrom the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
−4≤x≤1.
From the graph, we have
f(-4) = -4
f(1) = 4
The average rate of change at this interval is calculated as
Rate = Change in function values/Change in x values
So, we have
Rate = (-4 - 4)/(-4 - 1)
Evaluate
Rate = 1.6
Hence, the rate is 1.6
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Kim bought a birdhouse that originally cost $36. She used a coupon that took 25% off the price. How much money did Kim save?
Kim saved $9 by using the coupon.
How to find Original price?
The MSRP (i.e., Manufacturer's Suggested Retail Price) set the original price, which is the cost. In the majority of cases, the original price would have been less expensive than the current price, though this is not always the case. Finding an item's original price and knowing the price after a discount are both made possible by original price.
Original price = Sales price/(100%-Discount%)
To find out how much money Kim saved, we need to first find out how much the birdhouse cost after the coupon was applied.
The coupon took 25% off the original price, so the birdhouse cost 100% - 25% = 75% of its original price.
So, the new price of the birdhouse would be:
36 * 75% = $27
Kim saved 36 - 27 = $9 by using the coupon.
Therefore, Kim saved $9 using the coupon.
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suppose that random sample in the previous question yielded these observed scores: 6 12 5 10 6 9 12 20 5 23 10 20 11 28 13 18 find the 99% confidence interval
If random sample yielded these observed scores: 6 12 5 10 6 9 12 20 5 23 10 20 11 28 13 18. The 99% confidence interval for the mean height of both groups combined is approximately (3.92, 20.58) cm.
To calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution, since the sample size is relatively small (less than 30) and the population standard deviation is unknown.
First, we need to calculate the sample mean and sample standard deviation. The sample mean can be calculated by adding up all the observed scores and dividing by the total number of scores. In this case, the sample mean is (6+12+5+10+6+9+12+20+5+23+10+20+11+28+13+18) / 16 = 12.25 cm.
The sample standard deviation can be calculated using the formula:
s = √((∑(x - x')^2) / (n - 1))
where x is each observed score, x' is the sample mean, and n is the sample size. In this case, the sample standard deviation is approximately 7.05 cm.
Next, we need to calculate the t-value for a 99% confidence level, with 15 degrees of freedom (16 - 1). Using a t-table or a statistical software, we can find that the t-value is approximately 2.947.
Finally, we can calculate the confidence interval using the formula:
Confidence interval = sample mean ± (t-value * (sample standard deviation / √(sample size)))
Plugging in the values, we get:
Confidence interval = 12.25 ± (2.947 * (7.05 / √(16))) = 12.25 ± 8.33
In summary, to calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution and the formula for confidence intervals. We need to calculate the sample mean, sample standard deviation, t-value for the desired confidence level, and then plug these values into the formula to get the confidence interval.
This interval represents the range of values within which we can be 99% confident that the true mean height of both groups combined falls.
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The graph shows the total points earned for several pairs of shoes. The initial number of points earned when signing up is ________. The number of points earned per pair of shoes purchased is _________.
The initial number of points earned when signing up is 30 and earned per pair of shoes purchased is 15.
What is the equation of a line passing through two points?Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,
[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]
Let 'x' be the number of shoes purchased and 'y' be the total points earned.
From the graph, the two points are (2, 60) and (4, 90). Then the equation is given as,
[tex]\rm (y - 60) = \left (\dfrac{90 - 60}{4 - 2} \right) (x - 2)[/tex]
y - 60 = 15(x - 2)
y - 60 = 15x - 30
y = 15x + 30
The initial number of points earned when signing up is 30 and earned per pair of shoes purchased is 15.
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consider the following regression model: which of the following is an algebraic property of ols estimates of this model and its associated statistics? group of answer choices the sum, and therefore the sample average of the ols residuals, is positive. the sum of the ols residuals is negative. the sample covariance between the regressors and the ols residuals is zero. ols sample regression line always passes through the sample average of x and sample average of y both a and b are correct both a and d are correct both c and d are correct none of the above
Option (c) is correct: the sample covariance between the regressors and the OLS residuals is zero. This is an important property because it implies that the OLS estimator is not biased and the estimated coefficients of the independent variables are consistent.
The algebraic property of OLS (Ordinary Least Squares) estimates is that the sample covariance between the regressors and the OLS residuals is zero. This means that the OLS estimates are unbiased and not correlated with the independent variables in the regression model.
Option (a) is incorrect: the sum, and therefore the sample average of the OLS residuals, can be either positive or negative depending on the distribution of the data and the fit of the model.
Option (b) is also incorrect: the sum of the OLS residuals can be either positive or negative depending on the distribution of the data and the fit of the model.
Option (d) is incorrect: the OLS sample regression line does not always pass through the sample average of x and the sample average of y. However, it does pass through the point of averages when the model includes a constant term (i.e., intercept).
Therefore, the correct answer is (c): the sample covariance between the regressors and the OLS residuals is zero.
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If x + y = 6 and 3x – y = 4 then x – y is equal to
Answer:
[tex]-1[/tex]
Step-by-step explanation:
[tex](x+y)+(3x-y)=4 \implies 4x=10 \implies x=2.5 \\ \\ 2.5+y=6 \implies y=3.5 \\ \\ \therefore x-y=2.5-3.5=-1[/tex]
x4-8x2y2+16y4-256 Factorise the equation
Answer:
it's like this the answer
Step-by-step explanation:
x⁴-8x²y²+16y²-256
(x²-8xy)²+(4y-16)²
Answer:
x⁴-8x²y²+16y²-256
(x²-8xy)²+(4y-16)²
Step-by-step explanation:
Which property of real numbers is shown below?
3 + ((-5) + 6) = (3 + (-5)) + 6
O commutative property of addition
O identity property of multiplication
associative property of addition
commutative property of multiplication
3
David and Alec are comparing the international calling plans on their cell phones. On his plan,
David pays $4 just to place a call and $1 for each minute. When Alec makes an international
call, he pays $1 to place the call and $2 for each minute. A call of a certain duration would
cost exactly the same under both plans. What is the duration?
Write a system of equations, graph them, and type the solution.
a certain species of virulent bacteria is being grown in a culture. it is observed that the rate of growth of the bacterial population is proportional to the number present. if there were 4000 bacteria in the initial population and the number doubled after the first 30 minutes, how many bacteria will be present after 3 hours?
For a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
What is exponential function?A mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decline or exponential growth, and so forth.
When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. It is intended for the quick growth to be a "exponential increase".
The species of bacteria follow an exponential growth pattern.
The exponential growth is given as:
[tex]A(t) = A_0e^{kt}[/tex]
Where, A₀ is the initial population = 4000
k = constant
t = time = 30 minutes = 1/2 hour.
The bacteria doubles in 30 minutes, thus A(t) = 2(4000) = 8000.
Substituting the values in the equation:
[tex]8000 = 4000e^{k(\frac{1}{2} )}\\\\2 = e^{k(\frac{1}{2} )}[/tex]
Takin ln on both sides of the equation:
ln(2) = 1/2 k
2(ln(2)) = k
k = 1.38
The number of bacteria present after 3 hours:
[tex]A(t) = 4000e^{(1.38)(3)}\\\\[/tex]
A(t) = 256000
Hence, for a certain species of virulent bacteria with the rate of growth of the bacterial population as proportional to the number the bacteria present after 3 hours is 256000.
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Use the Slope Formula to calculate the slope of a line with these two points. Find the slope of the line that passes through (5, 11) and (9, 2).
lThe table below shows the price of different quantities
of standard-sized lemons at Joe's Fruit Stand. What is the
least amount of money needed to purchase exactly 20
standard-sized lemons if the bags must be sold intact
and there is no tax charged for lemons?
Number of lemons:
Total price:
$3.60
1
$0.30
bag of 6
$1.20
bag of 12
$2.10
The least amount of money needed to purchase exactly 20 standard-sized lemons is $1.50, by buying three bags of 6 lemons each and two individual lemons.
What is Combination?
In mathematics, a combination is a way of selecting items from a larger set without regard to the order in which the items are selected. In other words, a combination is a selection of a subset of items from a larger set, where the order of the selected items does not matter.
The number of possible combinations of r items selected from a set of n items is denoted by the notation C(n, r), or sometimes written as nCr. The formula for calculating the number of combinations is:
C(n, r) = n! / (r! * (n - r)!)
To purchase exactly 20 standard-sized lemons at Joe's Fruit Stand, we need to find the combination of bags of lemons that adds up to a total of 20. We want to minimize the cost, so we should choose the combination of bags with the lowest cost.
One possible combination is to buy two bags of 12 lemons each, for a total of 24 lemons, and then discard 4 lemons. This would cost $2.10 x 2 = $4.20.
Another possible combination is to buy three bags of 6 lemons each, for a total of 18 lemons, and then buy two individual lemons for a total of 20 lemons. This would cost $0.30 x 3 + $0.30 x 2 = $1.50.
Therefore, the least amount of money needed to purchase exactly 20 standard-sized lemons is $1.50, by buying three bags of 6 lemons each and two individual lemons.
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in how many ways can a president, vice-president, and treasurer be chosen from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions? on person cannot serve in more than one position
The total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman is 314 ways.
We can approach this problem using the principle of inclusion-exclusion.
First, let's find the total number of ways to choose a president, vice-president, and treasurer from a group of 8 people without any restrictions. We can do this by using the permutation formula:
8P₃ = 8 x 7 x 6 = 336
Next, let's find the number of ways to choose the three positions where only freshmen are chosen. There are 4 freshmen to choose from, so we can select the president, vice-president, and treasurer in 4P₃ = 4 x 3 x 2 = 24 ways.
Similarly, there are 4 sophomores to choose from, so we can select the three positions where only sophomores are chosen in 4P₃ = 4 x 3 x 2 = 24 ways.
However, we have overcounted the cases where only freshmen or only sophomores are chosen, since the problem statement requires that at least one freshman and at least one sophomore hold at least one of the three positions. Therefore, we need to subtract the number of cases where only freshmen or only sophomores are chosen.
There is only one way to select the president, vice-president, and treasurer from the 4 freshmen, and likewise, there is only one way to select them from the 4 sophomores. Therefore, there are a total of 2 ways to select the three positions where only one class is represented.
Finally, we need to add back the cases where no freshman or no sophomore is chosen. This occurs only if all three positions are filled by juniors or seniors. There are 4 juniors and seniors to choose from, so we can select the three positions in 4P₃ = 4 x 3 x 2 = 24 ways.
Therefore, the total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions is:
336 - 24 - 24 + 2 + 24 = 314 ways.
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3x - 5 = -3 is the answer positive or negative
Answer:
x = 2/3
0r 0.6(6)
both are positive
Step-by-step explanation:
3x - 5 = -3 is the answer positive or negative?
3x - 5 = -3
3x = -3 + 5
3x = 2
x = 2/3
0r 0.6(6)
Each of four friends-Jennifer, Rebecca, Derek, and
Matthew-had the goal of raising $50. How much
money did each person raise? Show or explain your
answer
a. Jennifer raised 50% of her goal.
b. Rebecca raised 100% of her goal.
c. Derek raised 75% of his goal.
d. Matthew raised 150% of his goal.
Answer:
Jennifer raised $25
Rebecca raised £50
Derek raised $37.50
Matthew raised $75
Step-by-step explanation:
J: 50% = dividing by 2, 50/2= 25
R: 50 is 100%, because that was the total
D: 75% = dividing by 4, timsing by three, so 50/4 is 12.5 x 3 is 37.5, put it into currency $37.50
M: We add another 25% onto 50 so 25+50=75.
(hope this works!!)
3+2y equals square root of -y
The solution to the given quadratic equation formed is; y = -9/4 and y = -1
How to find the solution to the quadratic equation?The given equation is expressed as;
(3 + 2y) = √(-y)
Taking the square of both sides gives us;
(3 + 2y)² = √(-y)]²
→ 9 + 12y + 4y² = -y
4y² + 13y + 9 = 0
Factoring the expression gives us;
4y² + 4y + 9y + 9 = 0
4y(y + 1) + 9(y + 1) = 0
Thus;
(4y + 9) = 0
(y + 1) = 0
y = -9/4
y = -1
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Given f(x)=4x^2+9x+9, find f(−1)
The value of the function f(-1) is -4
What is a function?A function is simply described as an equation that explains the relationship between the independent variable and the dependent variable.
From the information given, we have the function;
f(x)=4x^2+9x+9
To determine the value of f(-1)
substitute the value of x as- 1, we get;
f(-1) = 4(-1)² + 9(-1) + 9
expand the bracket, we get;
f(-1) = -4 -9 + 9
Add or subtract the values, we have;
f(-1) = -4
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Which procedure correctly simplifies the expression 2(4x + 3) + (x - 3)?
To simplify the expression 2(4x + 3) + (x - 3), we need to use the distributive property of multiplication over addition, and then combine like terms.
The expression 2(4x + 3) + (x - 3) contains parentheses and addition and multiplication operations, so we need to follow the order of operations to simplify it. The order of operations is:
1. Simplify any expressions inside parentheses.
2. Evaluate any exponents.
3. Perform multiplication and division, from left to right.
4. Perform addition and subtraction, from left to right.
Let's follow these steps to simplify the expression,
1. Simplify any expressions inside parentheses.
There are two sets of parentheses in the expression: (4x + 3) and (x - 3).
We can use the distributive property of multiplication over addition to eliminate the parentheses:
2(4x + 3) + (x - 3) = 8x + 6 + x - 3
2. Evaluate any exponents,
There are no exponents in the expression.
3. Perform multiplication and division, from left to right.
There is no multiplication or division to perform.
4. Perform addition and subtraction, from left to right.
We can now simplify the expression by combining like terms:
8x + 6 + x - 3 = (8x + x) + (6 - 3) = 9x + 3
Therefore, the simplified expression is 9x + 3.
In summary, the correct procedure to simplify the expression 2(4x + 3) + (x - 3) is to use the distributive property to eliminate the parentheses, and then combine like terms to obtain the simplified expression 9x + 3.
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Skye’s grandparents invest $1500 in a college account. It earns 4. 9% interest that is compounded annually. How much money will be in the account after 10 years?
Round to the nearest cent, if necessary
The total amount accrued, principal plus interest, with compound interest on a principal of $ 1,500.00 at a rate of 4.9 % per year compounded 1 times per year over 10 years is $2,420.17.
Using the compound interest formula is
Compound interest is calculated by multiplying the initial principal amount (P) by one plus the annual interest rate (R) raised to the number of compound periods (nt) minus one.
[tex]$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{r}}{\mathrm{n}}\right)^{\mathrm{nt}}$[/tex]A= Total amount =?
P= Principal amount = 1500
r=Rate of interest =4.9 %=0.049
t= time =10years
n= compounding = annually =1
Using the above data and formula, we get:
First, convert R as a percent to r as a decimal
[tex]& \mathrm{r}=\frac{\mathrm{R}}{100} \\[/tex]
[tex]& \mathrm{r}=\frac{4.9}{100} \\[/tex]
[tex]& \mathrm{r}=0.049 \text { rate per year, }[/tex]
Then solve the equation for A
[tex]& \mathrm{A}=1,500.00\left(1+\frac{0.049}{1}\right)^{(1)(10)} \\[/tex]
[tex]& \mathrm{A}=1,500.00(1+0.049)^{10} \\[/tex]
[tex]& \mathrm{~A}=\$ 2,420.17[/tex]
The total amount accrued after 10 years is $2,420.17.
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PROMPT: A spherical toy of diameter 75 cm must have a triangular sticker of height 12 cm and base of 10 cm. What is the surface area not covered by the sticker?
CLAIM:
EVIDENCE:
REASONING:
The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
CLAIM: The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
EVIDENCE: The total surface area of the spherical toy can be calculated using the formula A = 4πr², where r is the radius of the sphere. Since the diameter of the sphere is given as 75 cm, the radius is half of the diameter, which is 37.5 cm. Therefore, the total surface area of the spherical toy is:
A = 4π(37.5)²
A = 4π(1406.25)
A ≈ 17593.29 cm²
The surface area covered by the triangular sticker can be calculated by finding the area of the triangle, which is given by the formula A = 1/2 bh, where b is the base and h is the height. Therefore, the surface area covered by the sticker is:
A = 1/2 (10)(12)
A = 60 cm²
The surface area not covered by the sticker is the difference between the total surface area of the spherical toy and the surface area covered by the sticker:
A_not_covered = A - A_sticker
A_not_covered ≈ 17593.29 - 60
A_not_covered ≈ 17533.29 cm²
Therefore, the surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².
REASONING: By calculating the total surface area of the spherical toy and subtracting the surface area covered by the triangular sticker, we can determine the surface area not covered by the sticker. Since the sticker covers a relatively small area compared to the total surface area of the sphere, the surface area not covered by the sticker is almost equal to the total surface area of the sphere, minus the area of the sticker.
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a system if equations y=x-6 and y=-x-2 grap the sytsem then write the solution you can also awnser no soloution or infinite solutions.
the solution is where they intercept; (2,-4)
What’s the answer for this I’m not sure
Answer:
8√57/57
Step-by-step explanation:
a² + b² = c²
a² + 8² = 11²
a² + 64 = 121
a² = 57
a = √57
For angle Θ, opp = 8, adj = √57, hyp = 11.
tan Θ = opp/adj = 8/√57 = 8√57/57
The stock price of Company A decreased by $1.27 every day for 4
days. The fifth day, the stock price increased by $3.47. What was
the total change in the stock's price over 5 days?
Answer:
Step-by-step explanation:
The stock price of Company A decreased by $1.27 for 4 days, so the total decrease in the stock's price would be $1.27 * 4 = $5.08.
On the fifth day, the stock price increased by $3.47, so the total change in the stock's price over 5 days would be $3.47 - $5.08 = -$1.61.
So the total change in the stock's price over 5 days was a decrease of $1.61.
Which angles are corresponding angles? Se
lect all that apply
The angles that are corresponding angles:
∠1 and ∠3
∠5 and ∠7
∠6 and ∠8
We know that when a transversal intersects parallel lines or non-parallel lines then the angles formed at the same relative position at each intersection are nothing but the corresponding angles.
If a transversal intersects parallel lines, then the corresponding angles formed have equal measure.
Wheras if a transversal intersects non-parallel lines, then the corresponding angles formed doesn’t have any relation with each other.
In the following figure we can observe that line p and line q are non-parallel lines and are intersected by transversal r.
From definition of corresponding angles, the pair of corresponding angles:
∠1 and ∠3
∠5 and ∠7
∠6 and ∠8
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Find the complete question below.
given that x=a,y=b is the solution to the system of equations 2x+y=4, x-y=5 then what is the value of b to the power of a
Answer:
The answer is -8
Step-by-step explanation:
[tex]2x+y=4\\x-y=5\\\\[/tex]
after combining these into a singular equation, we get:
[tex]3x=9\\x=3[/tex]
substitute the value of [tex]x[/tex] into one of the equations:
[tex]x-y=5\\3-y=5\\y=-2[/tex]
now that we found the [tex]x[/tex] and [tex]y[/tex] value, we can substitute it into the term [tex]b^a[/tex] since we know that [tex]x=a[/tex] and [tex]y=b[/tex].
[tex]a^b\\a=x, b=y\\x=3, a=3\\y=-2, b=-2\\-2^3\\-8[/tex]
THERES A PICTURE
HELP ME PLEASEEEEE AND THANK YOUUUUU
The equation of the quadratic curve are:
Curve 1: y = -(x + 5)² + 4Curve 2: y = (x + 5)² + 4How to write the equation of parabolaQuadratic equation when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k where a = 1/4p
The vertex for curve 1
v (h, k) = (-5, 4)
h = -5
k = 4
substitution of the values into the equation gives
y = a(x - h)² + k
y = a(x + 5)² + 4
Using (-3, 0) to solve for a
y = a(x + 5)² + 4
0 = a(-3 + 5)² + 4
-4 = a (2)²
a = -1
The equation is y = -(x + 5)² + 4
The vertex for curve 2
v (h, k) = (5, -4)
h = 5
k = -4
substitution of the values into the equation gives
y = a(x - h)² + k
y = a(x - 5)² - 4
Using (3, 0) to solve for a
y = a(x - 5)² - 4
0 = a(3 - 5)² - 4
4 = a (-2)²
a = 1
The equation is y = (x + 5)² + 4
Learn more about vertex of quadratic equations at:
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