Question

A player kicks a soccer ball off of the ground. The height of the ball is modeled by the equation h(t)=-\frac34\left(t-4\right)^2+12h(t)=− 3/4 (t−4)^2 +12.
After how many seconds does the ball hit the ground?

Answer 1

Answer:

Step-by-step explanation:

We can solve this in either of two approaches:  Mathematically or Graphically.

Mathematically

y=-(3/4)(x-4)^2+12  where y is the height of the ball, and x is the time, in seconds.

We want to know how many seconds for the height to be 0, so y=0.

0 = -(3/4)(x-4)^2+12

-12 = -(3/4)(x-4)^2

12*(4/3) = (x-4)^2

16 = (x-4)^2

x = 8 and 0 (the initial point).]

It will reach the ground in 8 seconds

Graphically

Plot the function and find the time, x, when the graph passes through the x axis (after t = 0).  Attached.