Question

Heidi bought a machine that throws tennis balls for her dog to fetch. The height of each ball thrown by the machine, in feet, is modeled by the function f(x)=−x²+x+2, where x represents time in seconds. How many seconds after the machine throws the ball does it hit the ground?

a) 3 seconds

b) 4 seconds

c) 2 seconds

d) 1 second

Answer 1

By setting the height function to zero and solving for time x, we find that the tennis ball thrown by the machine hits the ground after 2 seconds.

Step-by-step explanation:

To determine how many seconds after the machine throws the ball it hits the ground, we need to find the value of time x when the height is zero, which is when the ball touches the ground. The height function given is f(x) = -x2 + x + 2. We set this equation equal to zero and solve for x.

0 = -x2 + x + 2

By factoring or using the quadratic formula, we can find the roots of the equation:

• (x + 1)(x - 2) = 0

This yields two values for x: x = -1 and x = 2. Since time can't be negative, we discard x = -1 and accept x = 2 as the time the ball takes to hit the ground. Therefore, the answer is (c) 2 seconds.