Algebra 2 Word Problem. Would be grateful for explanation.

Question

You hit a tennis ball straight up into the air with a tennis racket. The ball has an upward velocity of 46 feet per second. The point of contact between the tennis racket and ball is 4 feet above the ground. The function h=-16t^2+46t+4 gives the height h (in feet) of the tennis ball after t seconds. At what time will the ball be 3 feet off the ground? Give your answer rounded to the nearest thousandth.

Answer 1

h(t) = -16t² + 46t + 4

For h = 3:

3 = -16t² + 46t + 4

0 = -16t² + 46t + 1

Use the quadratic formula and your calculator to get the answer. You'll get two values for t (in seconds), one positive and one negative. Since we can't go back in time, the positive answer is the correct one.