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.

Answer 1

so what is the question ?

Answer 2

full question (please post this next time):

The path of a football kicked by a field goal kicker can be modeled by the equation y = –0.03x^2 + 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. yds. How far is the football kicked? yds.

Answer 3

there's a couple of ways you could do this

easiest would be to use a graphing calculator and determine the vertex (maximum height) and x-intercept (the length that the football is kicked). however, this may not be an option on examinations, so it would be best to also learn how to calculate it manually

to find the vertex, we can convert the equation to vertex form

for a generic quadratic equation in y = ax^2 + bx + c form, the vertex has the x-coordinate
-b/(2a)

apply this to your equation y = –0.03x^2 + 1.53x to determine the x-coordinate of the vertex

from there, simply plug that x-coordinate back into the equation to determine the y-value of that vertex, or in other words, the maximum height travelled

for the horizontal distance, you want to set y = 0 and solve for the x-intercepts using the quadratic formula

I know this is a lot, so please let me know if you're stuck on any steps or want to check your solution