The motion of the object which is described by the quadratic equation is a projectile motion, and the horizontal distance the object travels is 20 feet .
Projectile motion is the motion of an object which is thrust into the air and moves under the effect of gravitational force alone.
The equation in the question is; y = -x² + 16·x + 80
Where;
y = The vertical distance above the ground
x = The horizontal distance of the object
y = -x² + 16·x + 80
From which we get;
When the object hits the ground, y = 0, which indicates;
y = 0 = -x² + 16·x + 80
The value of x that is a solution to the above equation represents the distance the object travels before it reaches the ground.
-x² + 16·x + 80 = 0
x² - 16·x - 80 = 0
(x - 20)·(x + 4) = 0
x = 20 or x = -4
The distances at which the object reaches the ground are x = -4 feet or x = 20 feet
The possible distance the object will travel in the horizontal direction is 20 feet.
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