Question 970710: A football is kicked at 40 yards away from a goal post that is 10 feet high.
Its path is modeled by y = -0.03x^2 + 1.6x, where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet.
Does the football go over the goal post? How far above or below the goal post is the football?
Use two or more complete sentences to explain your answers.
(Hint: The unit conversion is built into the given function.)
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A football is kicked at 40 yards away from a goal post that is 10 feet high.
Its path is modeled by y = -0.03x^2 + 1.6x, where x is the horizontal distance in yards traveled by the football and y is the corresponding height above the ground in feet.
Does the football go over the goal post? How far above or below the goal post is the football?
Use two or more complete sentences to explain your answers.
(Hint: The unit conversion is built into the given function.)
.
The problem gives us the relation of the "height" (y) relative to the "distance" (x). Therefore, all we need to do is substitute the x with 40 and see the calculated 'y' is 10 or greater.
.
y = -0.03x^2 + 1.6x
y = -0.03(40)^2 + 1.6(40)
y = -0.03(1600) + 64
y = -48 + 64
y = 16 feet
So, since this is greater than 10 feet:
Does the football go over the goal post? yes
How far above or below the goal post is the football? 6 feet above
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