The height, $h ( x )$ , of a punted rugby ball is given by
$h ( x ) = \frac { 1 } { 64 } x ^ { 2 } + \frac { 13 } { 32 } x + 2$
where x is the horizontal distance in feet from the point where the ball is punted. How far, horizon- tally, is the ball from the kicker when it is at its highest point?
A) 28 feet
B) 13 feet
C) 18 feet
D) 23 feet
E) 16 feet

Question

The height, $h ( x )$ , of a punted rugby ball is given by 
$h ( x ) = \frac { 1 } { 64 } x ^ { 2 } + \frac { 13 } { 32 } x + 2$ 
where x is the horizontal distance in feet from the point where the ball is punted. How far, horizon- tally, is the ball from the kicker when it is at its highest point? 
A) 28 feet
B) 13 feet
C) 18 feet
D) 23 feet
E) 16 feet

Quizplus · Accepted Answer

The highest point of a quadratic function $ax^2 + bx + c$ is at $x = -\frac{b}{2a}$. Here, $a = \frac{1}{64}$ and $b = \frac{13}{32}$. Calculating gives $x = -\frac{\frac{13}{32}}{2 \times \frac{1}{64}} = 13$ feet.

The Height h(x)h ( x )h(x) , of a Punted Rugby Ball Is Given By

The Height $h ( x )$ , of a Punted Rugby Ball Is Given By