Answer: 0 ft, maximum, 11.6 ft, 6.8 ft, 13.6 ft
Step-by-step explanation:
y = -0.25x² + 3.4x
a= -0.25 b = 3.4 c = 0
"c" is the initial height = 0
"a" is negative ⇒ ∩-shaped parabola ⇒ vertex is a maximum
Axis of Symmetry (horizontal distance at maximum):
[tex]x=\dfrac{-b}{2a}=\dfrac{-(3.4)}{2(-0.25)}=\dfrac{-3.4}{-0.5}\quad = \large\boxed{6.8}[/tex]
Maximum: (heighth at maximum)
y = -0.25(6.8)² + 3.4(6.8)
= -11.56 + 23.12
= 11.56
Zeros (when the ball is on the ground):
0 = -0.25x² + 3.4x
0 = x(-0.25x + 3.4)
0 = x 0 = -0.25x + 3.4
-3.4 = -0.25x
[tex]\dfrac{-3.4}{-0.25}=x[/tex]
13.6 = x
x = 0 is where the ball started
x = 13.6 is where the ball landed
