Question

H(t)=−(t−7)²+4

Answer 1

Answer:

1.  smaller value of t = 5

   larger value of t = 9

2.  (7, 4)

Step-by-step explanation:

Given function:  $h(t)=-(t-7)^2+4$

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

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

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

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