Solved on Sep 19, 2023

Write a parabola equation in intercept form with $x$ -intercepts at -4 and -8, passing through $(-3,20)$ .

STEP 1

Assumptions1. The x-intercepts of the parabola are -4 and -8. . The parabola passes through the point (-3,20).
3. The general form of a parabola in intercept form is $y=a(x-h)(x-k)$ , where h and k are the x-intercepts.

STEP 2

First, we need to write the general form of the parabola using the given x-intercepts. $y=a(x+4)(x+8)$

STEP 3

We know that the parabola passes through the point (-3,20). We can substitute these values into the equation to solve for a.
$20=a(-3+)(-3+8)$

STEP 4

implify the equation.
$20=a(1)()$

STEP 5

olve for a.
$a=20/5$

STEP 6

Calculate the value of a.
$a=4$

STEP 7

Now that we have the value of a, we can write the final equation of the parabola.
$y=4(x+4)(x+)$ The equation of the parabola in intercept form is $y=4(x+4)(x+)$ .

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Write a parabola equation in intercept form with $x$ -intercepts at -4 and -8, passing through $(-3,20)$ .

STEP 1

Assumptions1. The x-intercepts of the parabola are -4 and -8. . The parabola passes through the point (-3,20).
3. The general form of a parabola in intercept form is $y=a(x-h)(x-k)$ , where h and k are the x-intercepts.

STEP 2

First, we need to write the general form of the parabola using the given x-intercepts. $y=a(x+4)(x+8)$

STEP 3

We know that the parabola passes through the point (-3,20). We can substitute these values into the equation to solve for a.
$20=a(-3+)(-3+8)$

STEP 4

implify the equation.
$20=a(1)()$

STEP 5

olve for a.
$a=20/5$

STEP 6

Calculate the value of a.
$a=4$

STEP 7

Now that we have the value of a, we can write the final equation of the parabola.
$y=4(x+4)(x+)$ The equation of the parabola in intercept form is $y=4(x+4)(x+)$ .

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Write a parabola equation in intercept form with xxx-intercepts at -4 and -8, passing through (−3,20)(-3,20)(−3,20).

STEP 1

Assumptions1. The x-intercepts of the parabola are -4 and -8. . The parabola passes through the point (-3,20).3. The general form of a parabola in intercept form is y=a(x−h)(x−k)y=a(x-h)(x-k)y=a(x−h)(x−k), where h and k are the x-intercepts.

STEP 2

First, we need to write the general form of the parabola using the given x-intercepts.y=a(x+4)(x+8)y=a(x+4)(x+8)y=a(x+4)(x+8)

STEP 3

We know that the parabola passes through the point (-3,20). We can substitute these values into the equation to solve for a.20=a(−3+)(−3+8)20=a(-3+)(-3+8)20=a(−3+)(−3+8)

STEP 4

implify the equation.20=a(1)()20=a(1)()20=a(1)()

STEP 5

olve for a.a=20/5a=20/5a=20/5

STEP 6

Calculate the value of a.a=4a=4a=4

STEP 7

Now that we have the value of a, we can write the final equation of the parabola.y=4(x+4)(x+)y=4(x+4)(x+)y=4(x+4)(x+)The equation of the parabola in intercept form is y=4(x+4)(x+)y=4(x+4)(x+)y=4(x+4)(x+).

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Write a parabola equation in intercept form with $x$ -intercepts at -4 and -8, passing through $(-3,20)$ .

Assumptions1. The x-intercepts of the parabola are -4 and -8. . The parabola passes through the point (-3,20).
3. The general form of a parabola in intercept form is $y=a(x-h)(x-k)$ , where h and k are the x-intercepts.

First, we need to write the general form of the parabola using the given x-intercepts. $y=a(x+4)(x+8)$

We know that the parabola passes through the point (-3,20). We can substitute these values into the equation to solve for a.
$20=a(-3+)(-3+8)$

implify the equation.
$20=a(1)()$

olve for a.
$a=20/5$

Calculate the value of a.
$a=4$

Now that we have the value of a, we can write the final equation of the parabola.
$y=4(x+4)(x+)$ The equation of the parabola in intercept form is $y=4(x+4)(x+)$ .