Question

f(t)=t^{2}+19t + 60

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

$t^2 + 19t = 0$

Step2: Factor the equation

$t(t + 19) = 0$

Step3: Solve for t

$t = 0$ or $t = -19$

Step4: Find vertex t-coordinate

$t = -\frac{b}{2a} = -\frac{19}{2(1)} = -9.5$

Step5: Compute vertex y-coordinate

$f(-9.5) = (-9.5)^2 + 19(-9.5) = -90.25$

Answer:

smaller t = -19
larger t = 0
(-9.5, -90.25)