Question

g(t)=(t - 10)(t + 1)

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 function to zero

$(t - 10)(t + 1) = 0$

Step2: Solve for t values

$t - 10 = 0 \Rightarrow t = 10$; $t + 1 = 0 \Rightarrow t = -1$

Step3: Determine smaller and larger t

Smaller t = -1, larger t = 10

Step4: Find axis of symmetry (t-vertex)

$t = \frac{-1 + 10}{2} = 4.5$

Step5: Calculate g(4.5) for vertex

$g(4.5) = (4.5 - 10)(4.5 + 1) = (-5.5)(5.5) = -30.25$

Answer:

smaller t = -1
larger t = 10
(4.5, -30.25)