Question

A ball is thrown into the air. The height h, in feet, of the ball after x seconds is given by the function h = −16(x − 2)2 + 72. What is the equation in standard form and the maximum height of the ball?

Answer 1

h = −16(x − 2)² + 72

= −16((x − 2)(x − 2)) + 72 expand the square (x - 2)² = (x - 2)(x - x)

= -16 ((x)(x) + (x)(-2) + (-2)(x) + (-2)(-2)) + 72

= -16 (x² + (-2x) + (-2x) + (4) ) + 72

= -16 (x² + (-4x) + (4) ) + 72

= -16 (x² - 4x + 4 ) + 72

= (-16)(x²) + (-16)(-4x) +(-16)(4) + 72

= -16x² + 64x - 64 + 72

= -16x² + 64x + 8 My guess is D ; 72 ???

I have no clue what the ; 72 means after the given answer. It must be a standard form thing I never learned.

Explanation:

Answer 2

A. -16x²+64x+8

B. 72 ft.

Step-by-step explanation: A. Expand the perfect square binomial -16(x²-4x+4)+72, dist. -16 (-16x²+64x-64+72), then combine like terms (-16x²+64x+8)

B. Find the abs. max. by looking back at the vertex form. The max is (2,72). Use the y-value for the height.