Chapter 9.2, Problem 14PPE

To determine

The equation of axis of symmetry and the coordinates of the vertex of the graph of each function.

Answer to Problem 14PPE

Equation of axis of symmetry: $x=-2$

  $\text{Vertex is }\left(-2,13\right)$

Explanation of Solution

Given:

The given function is:

  $y=-4x^2-16x-3$

Calculation:

Compare the given function with $y=a{x}^2+bx+c$ .

  $\begin{array}{l}here;\\ a=-4\\ b=-16\\ c=-3\end{array}$

  $\begin{array}{l}\text{Equation of axis of symmetry is:}\\ x=-\frac{b}{2a}\end{array}$

Therefore, the axis of symmetry is:

  $\begin{array}{l}x=-\frac{b}{2a}\\ x=\frac{-\left(-16\right)}{2\left(-4\right)}\\ x=-\frac{16}{8}\\ x=-2\end{array}$

The x-coordinate of the given function is $x=-2$ . Now, the y-coordinate will be:

  $\begin{array}{l}y=-4x^2-16x-3\\ y=-4{\left(-2\right)}^2-16\left(-2\right)-3\\ y=-16+32-3\\ y=13\\ So,\text{Vertex is }\left(-2,13\right)\end{array}$