Graphing Quadratic Equations: example 10.54

$h=\mathrm{-16}{t}^2+176t+4$

Since a is negative, the parabola opens downward.

The quadratic equation has a maximum.

1. ⓐ
   $\begin{array}{cccc}\text{Find the axis of symmetry.}\hfill & & & \begin{array}{c}t=-\frac{b}{2a}\hfill \\ t=-\frac{176}{2(\mathrm{-16})}\hfill \\ t=5.5\hfill \end{array}\hfill \\ & & & \text{The axis of symmetry is}t=5.5.\hfill \\ \text{The vertex is on the line}t=5.5.\hfill & & & \text{The maximum occurs when}t=5.5\text{seconds.}\hfill \end{array}$
2. ⓑ
   

   Find h when $t=5.5$.
   Use a calculator to simplify.
   		The vertex is $(5.5,488)$.
   Since the parabola has a maximum, the h-coordinate of the vertex is the maximum y-value of the quadratic equation.		The maximum value of the quadratic is 488 feet and it occurs when $t=5.5$ seconds.