Cecily is on her roof and wants to throw a ball straight up in the air and figure out how long it will take to reach the ground. The function that models an object falling to the ground is f(x) = -32x2 + vx + d. In this function, x is time, v is the initial (vertical) velocity in feet per second, and d is the initial distance above the ground in feet. If v is positive, then the initial velocity is upward. If v is negative, the initial velocity is downward. Write the function if Cecily releases the ball 40 feet above the ground at a velocity of 64 feet per second. Capture a screenshot of your graph and paste it below.

What does the maximum represent, and what is it?

What does the y-intercept represent, and what is it?

What do the x-intercepts represent, and what are they? Are they both useful?

How long will it take for the ball to hit the ground?

The force of gravity is different on Mars than on Earth. The function of the same situation on Mars would be represented by the function shown below. On which planet would the ball go highest? About how high would it go?