Question

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.

What is the football’s maximum height? Round to the nearest tenth.

Answer 1

Here's the actual equation: y = -0.03x^2 + 1.53x 25.5

Answer 2

The football’s maximum height is 19.5 yards

Explanation:

The equation presented is that of a parabolic function so the maximum height will be reached at vertex; at the vertex, x will be equal to half of the maximum horizontal distance, so the simplest way to solve this question, without resorting to derivatives is to find maximum horizontal distance, halve it, and apply it to the formula.

The maximum horizontal distance occurs when y=0:

`0 = -0.03x^(2) +1.53x\\0=x(-0.03x+1.53)\\x=(1.53)/(0.03)=51 \\`

Therefore, half of this value is 25.5 yards; applying it to the formula:

`y=-0.03*(25.5)^(2) +1.53*25.5\\y= 19.5`

The football’s maximum height is 19.5 yards