A boy is standing on a flat field and tosses his ball toward a second boy standing at the other end of the field. The path of the ball is a parabola, and the equation of the path is $f(x)=-4 x^{2}+8 x$. Based on this information, answer the question.
-What is the highest the ball will be above the flat field and for what value of $x$ ?
A) Highest height $=4$ when $x=2$
B) Highest height $=4$ when $x=1$
C) Cannot determine without additional information
D) None of the above

Question

Quizplus · Accepted Answer

The vertex form of a parabola $f(x) = ax^2 + bx + c$ gives the maximum height at $x = -\frac{b}{2a}$. Here, $a = -4$ and $b = 8$, so $x = 1$. Substituting $x = 1$ into the equation gives the highest height as 4.

A Boy Is Standing on a Flat Field and Tosses f(x)=−4x2+8xf(x)=-4 x^{2}+8 xf(x)=−4x2+8x

A Boy Is Standing on a Flat Field and Tosses $f(x)=-4 x^{2}+8 x$