Chapter 2.4, Problem 7E

To determine

To write: To write an equation of the parabola in vertex form.

Answer to Problem 7E

The equation of the parabola with the vertex $(-6,-12)$ and passes through $(0,-24)$ in vertex form is $y=-\frac{1}{3}{(x+6)}^2-12$ .

Explanation of Solution

Given information: Vertex $(-6,-12)$ and a point $(0,-24)$ .

Vertex form of a parabola is $y=a{(x-h)}^2+k$ .

Vertex $(h,k)$ is $(-6,-12)$ .

By substituting the vertex in the vertex form of equation we get,

  $y=a{(x+6)}^2-12$

To find the value of $a$ , substitute $(0,-24)$ in the above equation.

  $\begin{array}{c}$ -24=a{(0+6)}^2-12$$ -24=a{(6)}^2-12$-24=a(36)-12\\ -12=a(36)\\ a=\frac{-12}{36}=-\frac{1}{3}\end{array}$

Substitute $a=-\frac{1}{3}$ in $y=a{(x+6)}^2-12$ ,

  $y=-\frac{1}{3}{(x+6)}^2-12$

The above equation is the vertex form of the given parabola.