Problema Solution
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 provided by our tutors
1 ft = 1/3 yard
10 ft = 10/3 yards
y = - 0.03x^2 + 1.6x
to check if the football goes over over the post we need to find the value of y for x = 40
y = -0.03*40^2 + 1.6*40
y = 16
click here to see the step by step calculation for y
since y = 16 for x = 40 and 16 > 10/3 follows the football goes over the goal post
you can also come to the same conclusion by drawing the graph of y = - 0.03x^2 + 1.6x
click here to see the graph
How far above or below the goal post is the football?
we need to find the difference between the height of the ball and the height of the goal post
16 - 10/3 = (3*16 -10)/3 = 38/3 yards = 38 ft
the football goes 38 ft (or 12 2/3 yards) above the goal post.