Standard Form
This is a freefall question in feet so a = -16
Since it starts at 50 feet c = 50
So we have the equation f(x) = -16x^2 + bx + 50
plug in 1.5 for x and 88 for y to find b
88 = -16(1.5)^2 + 1.5b + 50
88 = 14 + 1.5b
74 = 1.5b
b = 148/3
f(x) = [tex]-16x^{2} +\frac{148x}{3} +50[/tex]
Vertex Form
the vertex is (h,k) or (1.5,88) since it is the highest point
f(x) = [tex]-16(x-1.5)^{2} + 88[/tex]
Graph
(see first picture at bottom)
Vertex
Vertex is (1.5, 88) since the maximum height is 88 at 1.5 seconds
Y-Intercept
y-intercept is 50 because it starts at 50 feet
Zeros
use quadratic formula (see second picture at bottom)
zeros = [tex]\frac{37}{24} +\frac{\sqrt{3169} }{24} and \frac{37}{24} -\frac{\sqrt{3169} }{24}[/tex]
= 3.8872 and -0.8039
zeroes represent when the ball hits the ground
