Answer:
6.3 yards high
Step-by-step explanation:
The three given points are (0,0), (1,6.86), and (2,3). Use these values in f(x) = ax2 + bx + c.
For (0,0), 0 = 0 + 0 + c.
So, c = 0.
For (1,6.86), 6.86 = a + b + c. Since c = 0:
a + b = 6.86(equation 1)
For (2,3), 3 = 4a + 2b + c. Since c = 0:
4a + 2b = 3(equation 2)
Multiply equation 1 by 2, and subtract the result from equation 2:
2a + 2b = 13.72
4a + 2b - (2a + 2b) = 3 - 13.72
2a = -10.72
a = - 5.36
Plug this value into equation 1:
-5.36 + b = 6.86
b = 12.22
So the function is f(x) = -5.36x2 + 12.22x.
When the ball hits the ground, the height is 0, or f(x) = 0:
Use the function to determine the height of the ball, f(x), after x = 1.5 seconds.
f(x) = -5.36x2 + 12.22x
= -5.36(1.5)2 + 12.22(1.5)
= 6.27
0 = -5.36x2 + 12.22x
0 ≈ x − 2.27(Divide both sides by -5.36x.)
x ≈ 2.27 ≈ 2.3
So, the ball will be about 6.3 yards high after 1.5 seconds.
