The path of a football kicked by a field goal kicker can be modeled by the equation y = - 0.03x2 + 1.53x, where x is the horizontal distance in yards and y is the corresponding height in yards.

Q1: What is the football's maximum height? Round to the nearest tenth.

Q2: How far is the football kicked?

Maximum height occurs when the velocity, derivative of the height function, is equal to zero ...

dy/dx=-0.06x+1.53, dy/dx=0 when 0.06x=1.53, x=25.5 yds

The maximum height is then found using this x in the height equation ...

h (25.5) = 19.5 (to nearest tenth)

I assume they want to know the maximum distance that the football travels before it hits the ground ... when h=0 that will represent total distance traveled when we solve for x ...

-0.03x^2+1.53x=0

1.53=0.03x

x=51 yds

You can find the distance kicked by solving for x:-

-0.03x^2 + 1.53x = 0

x (-0.03x + 1.53) = 0

x = 0 (this is the height when he first kicks)

-0.03x + 1.53 = 0

x = - 1.53 / - 0.03 = 51 yards

So Q2 is 51 yards