Kendall was playing t-ball and hit the ball off the tee, which is 3 feet off of the ground. If the equation h(t) = -16t2 + 20t + 3 represents the height of the ball at time t, what would the x-intercept represent in the context of this problem? Write your answer using complete sentences.

the x-intercept would be the time taken to hit the ground

Hmmm. I see h(t), but no x.

I expect you meant to ask what the t-intercept means. Reiny's answer would be the one you want.

Generally in problems like this, x represents the distance traveled horizontally. So, in that case, the x-intercept wold be how far away the ball hit the ground.

To determine the x-intercept of the equation h(t) = -16t^2 + 20t + 3, we need to find the value of t when h(t) equals zero. In the context of this problem, the x-intercept represents the time at which the height of the ball is zero.

To find the x-intercept, we set h(t) equal to zero and solve the equation:

-16t^2 + 20t + 3 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. Let's use the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

For this equation, a = -16, b = 20, and c = 3. Plugging these values into the quadratic formula, we have:

t = (-20 ± √(20^2 - 4(-16)(3))) / (2(-16))

Simplifying this equation gives us two possible solutions for t. Let's calculate them:

t = (-20 ± √(400 + 192)) / (-32)

t = (-20 ± √592) / (-32)

Now, using a calculator, we find the two values of t:

t ≈ 0.126 or t ≈ 1.874

Therefore, the x-intercept of the equation h(t) = -16t^2 + 20t + 3 represents the time when the height of the ball is zero. In the context of this problem, it means that Kendall hit the ball off the tee at approximately 0.126 seconds, and it reached the ground approximately 1.874 seconds after being hit.