Question

The height y (in feet) of a ball thrown by a child is

y=−1/16x²+6x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y when x=0)

Answer 1

To determine the height of the ball when it leaves the child's hand, substitute x = 0 into the equation y = -1/16x² + 6x + 3 to find that y = 3 feet.

Step-by-step explanation:

The height of the ball when it leaves the child's hand can be found by evaluating the equation y = −1/16x² + 6x + 3 at x = 0. Since this is the point where the ball is just thrown, the horizontal distance x will be zero. By substituting x = 0 into the equation, we obtain y = −1/16(0)² + 6(0) + 3, which simplifies to y = 3 feet. Therefore, the ball is 3 feet above the ground when it leaves the child's hand, since all other terms with x in them will be zero.