Henry throws a tennis ball over his house. The ball is 6 feet above the ground when he lets it go. The quadratic function that models the height, in feet, of the ball after t seconds is h = -16^2 + 46t + 6. Using the quadratic formula to solve, at what time does the ball hit the ground?

Please show all work and now just the answer.

Option C: It takes 3 seconds for the ball to hit the ground.

Explanation:

The given quadratic function is where h is the height in feet and t is the time in seconds.

We need to determine at what time the ball will hit the ground.

Time taken:

The time can be determined by substituting h = 0 in the function

Thus, we get;

Let us solve the quadratic expression using the quadratic formula.

Thus, we have;

Solving, we get,

Thus, the values of t are given by

and

and

and

Since, t cannot take negative values.

Thus, the value of t is

Hence, the time taken by the ball to hit the ground is 3 seconds.

Therefore, Option C is the correct answer.