Question

H(t)=−(t−7)²+4

Write the smaller t first, and the larger t second.

smaller t=?

larger t=?


2) What is the vertex of the parabola?

(?,?)

Answer 1

1. smaller value of t = 5

larger value of t = 9

2. (7, 4)

Explanation:

Given function:
`h(t)=-(t-7)^2+4`

To find the zeros, set the function to zero and solve for t:

`\begin{aligned}h(t) & =0\\\implies -(t-7)^2+4 & =0\\-(t-7)^2 & =-4\\(t-7)^2 & =4\\t-7 & =√(4)\\t-7 & =\pm 2\\t & =7\pm 2\\t & = 5,9\end{aligned}`

Vertex form:
`y=a(x-h)^2+k` where (h, k) is the vertex

Therefore, the vertex of the given function is (7, 4)