Answer :
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 .
What is a projectile motion?
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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