Answer: K
Step-by-step explanation:
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 or down will affect the intercepts and the maximum value of the vertex.
