Chapter 12: Q47. (page 637)

Write an equation for the parabola with the given vertex that passes through the given point.
Vertex $(0, 8)$
Point $(4, 0)$

Short Answer

Expert verified

The equation of the parabola is $y = - \frac{x^{2}}{2} + 8$ .

Step by step solution

Step 1. Given Information.

Given, a parabola has the vertex $(0, 8)$ and passes through the point $(4, 0)$ . The equation for the parabola is to be determined.

Step 2. Calculation.

The equation of a parabola with vertex $(h, k)$ is $y = a {(x - h)}^{2} + k$

Here h=0,k=8 and since the parabola passes through the point $(4, 0)$ , x=4,y=0

Plugging the values in the equation and solving for a:

$\begin{array}{l} y = a {(x - h)}^{2} + k \\ 0 = a {(4 - 0)}^{2} + 8 \\ a {(4)}^{2} = 0 - 8 \\ a (16) = - 8 \\ 16 a = - 8 \\ a = - \frac{8}{16} \\ a = - \frac{1}{2} \end{array}$

Plugging back the value of a, h and k in the equation:

$\begin{array}{l} y = - \frac{1}{2} {(x - 0)}^{2} + 8 \\ y = - \frac{x^{2}}{2} + 8 \end{array}$

Step 3. Conclusion.

Hence, the equation of the parabola is $y = - \frac{x^{2}}{2} + 8$ .

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Write an equation for the parabola with the given vertex that passes through the given point.
Vertex $(0, 8)$
Point $(4, 0)$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Write an equation for the parabola with the given vertex that passes through the given point.Vertex 0,8Point 4,0

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Mechanics Maths

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Write an equation for the parabola with the given vertex that passes through the given point.
Vertex $(0, 8)$
Point $(4, 0)$