Question

Mr. Howard is the most powerful jumper of the Howard family. When Mr. Howard jumps, his path through the air can be modeled by the equation y=-2(x-3) (x-7), where x is Mr. Howard's horizontal distance traveled (in feet) and y is his corresponding height (in feet). How far can Mr. Howard jump?

Answer 1

Mr. Howard's jump distance is determined by the horizontal distance between the paths where his parabolic jump intersects the ground, which is 4 feet according to the equation provided.

Step-by-step explanation:

Mr. Howard's jump distance can be determined by finding the horizontal distance between the points where the parabolic path of his jump intersects the ground level. The equation y = -2(x-3)(x-7) models his path, where x is the horizontal distance in feet and y is the height in feet. We can find the points where Mr. Howard's feet are on the ground by setting y to 0 and solving for x:

0 = -2(x-3)(x-7)

This gives us two points of intersection at x = 3 feet and x = 7 feet. The horizontal distance of Mr. Howard's jump is the difference between these two x-values. Thus, the total distance Mr. Howard can jump is 4 feet.