Question

a football is kicked into the air. The height of the football can be modeled by h=-16x^2 +32x, where h is the height reached by the ball after x seconds.

Answer 1

Your question is incomplete, here is the complete question;

A football is kicked into the air and follows the path defined by h=-2x^2+16x, where x is the time in seconds and h is the height in meters. What is the maximum height reached by the football?

Answer:

maximum height=h=32 meters

Step-by-step explanation:

The given equation is the equation of the parabola or quadratic equation.

The maximum height of the ball will occur at the axis of symmetry.

For the axis of symmetry let h=0,

so,

$-2x^2+16x=0$

comparing this equation to standard quadratic/parabola's equation, we get

a= -2, b=16 and c=0

Formula for axis of symmetry is x=-b/2a

x=-16/2*(-2)

x=-16/-4

x=4 it means axis of symmetry is vertical line through the point x=+4, so the maximum height will occur at x=+4

put x=4 to get maximum height as;

$h=-2(4)^2+16(4)$

$h=-2(16)+64\\\\h=-32+64\\\\h=32$

Maximum height$=h=32\ meter$