Q:

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. yds. How far is the football kicked? yds.

Accepted Solution

A:
This is the equation of an upside down parabola, so the maximum height will be at the vertex. To find the vertex, we'll use the formula for the x-coordinate and then solve for the y-coordinate.
[tex]x=\frac{-1.53}{2*-.03}=25.5[/tex]

Plugging this into the given formula:
[tex]y=-0.03(25.5)^2+1.53(25.5)=19.5075[/tex]
Since it asks us to round, the maximum height would be 20 yards. To find how far the football travels in total, we need to set the equation equal to 0 and find the roots:
[tex]0=-0.03x^2+1.53x=x(-0.03x+1.53)[/tex]

Then by the zero product property (or the no zero divisors rule), we have:
[tex]x=0[/tex] (this is the x value where the ball is kicked from)
[tex]-0.03x+1.53=0[/tex]
[tex]-0.03x=-1.53[/tex]
[tex]x=51[/tex]

So the ball travels 51 yards in total.