Question

A soccer ball is kicked in the air off a 22.0 meter high hill. The equation h(t)=-5t^2+10t+22 gives the approximated height h, in meters, of the ball t seconds after it is kicked. What equation can be used to tell if the ball reaches a height of 35 meters? Does the ball reach a height of 35 meters? How can you tell?

Equation:____
Answer:____​

Answer 1

Equation: 5t² − 10t + 13 = 0

Answer: No

Answer 2

Equation: 5t² − 10t + 13 = 0

Answer: No

Explanation:

h(t) = -5t² + 10t + 22

When h(t) = 35:

35 = -5t² + 10t + 22

5t² − 10t + 13 = 0

This equation must have at least one real solution if the ball is to reach a height of 35 meters. Which means the discriminant can't be negative.

b² − 4ac

(-10)² − 4(5)(13)

100 − 260

-160

The ball does not reach a height of 35 meters.