Chapter 9.5, Problem 67S

To determine

To find: The equation of the parabola for the given condition.

Answer to Problem 67S

The equation of the parabola for the given condition is $y=\frac{4}{3}{\left(x+3\right)}^2-4$ .

Explanation of Solution

Given information: The vertex is $\left(-3,-4\right)$ .

Calculation:

Since, the vertex is $\left(-3,-4\right)$ .

Thus, $h=-3,k=-4$ .

The equation of parabola is,

  $\begin{array}{l}y=a{\left(x-h\right)}^2+k\\ y=a{\left(x-\left(-3\right)\right)}^2+\left(-4\right)\\ y=a{\left(x+3\right)}^2-4\end{array}$

Substitute the values in above equation.

  $\begin{array}{l}8=a{\left(0+3\right)}^2-4\\ 8=9a-4\\ a=\frac{4}{3}\end{array}$

Substitute the values in above equation.

  $y=\frac{4}{3}{\left(x+3\right)}^2-4$