Compare the equations of: h = -t² + 4t + 5 and h = -t² + 4t + 12
h = -t² + 4t + 5:
c-value is 5
⇒ h-intercept is 5
intercept form: h = -(t + 1)(t - 5)
⇒ intercepts are t = -1 and t = 5
vertex form: h = -(x - 2)² + 9
⇒ vertex is (2, 9)
⇒ maximum value of h is 9
h = -t² + 4t + 12:
c-value is 12
⇒ h-intercept is 12
intercept form: h = -(t + 2)(t - 6)
⇒ intercepts are t = -2 and t = 6
vertex form: h = -(x - 2)² + 16
⇒ vertex is (2, 16)
⇒ maximum value of h is 16
The only value that changed between these two equations is "c", however the h-intercepts, maximum values, and t-intercepts are all different.
This is because the c-value shifted the entire parabola up. Shifting the parabola up <em>or down</em> will affect the intercepts and the maximum value of the vertex.
