Question

f(t)=(t - 5)^2-9

1. what are the zeros of the function?

write the smaller t first, and the larger t second.
smaller t=
larger t=

1. what is the vertex of the parabola?

Explanation:

Step1: Set f(t)=0

$(t - 5)^2 - 9 = 0$

Step2: Add 9 to both sides

$(t - 5)^2 = 9$

Step3: Take square roots

$t - 5 = \pm 3$

Step4: Solve for t

$t = 5 \pm 3$ → $t=2$ (smaller), $t=8$ (larger)

Step5: Identify vertex from form

Vertex form $a(t - h)^2 + k$ gives $(h,k)=(5,-9)$

Answer:

smaller t = 2
larger t = 8
(5, -9)