Question

Jesse tossed a paint brush off her roof. The height of the brush (in meters above the ground) t

seconds after Jesse tossed it is modeled by h(t) = -5(t)^2 + 5t + 10

Jesse wants to know when the brush will hit the ground.
1) Rewrite the function in a different form (factored or vertex) where the answer appears as a number in the equation.

h(t) =

2) How many seconds after being thrown does the brush hit the ground?

Answer 1

[AI-generated answer — Bot GPT 3.5]

1) First we factor out -5 from the equation to rewrite it in vertex form:

h(t) = -5(t^2 - t - 2)

Next, we factorize the quadratic equation inside the parentheses:

h(t) = -5(t - 2)(t + 1)

So, the function in factored form is h(t) = -5(t - 2)(t + 1).

2) To find when the brush hits the ground, we set h(t) = 0:

0 = -5(t - 2)(t + 1)

This means that the brush hits the ground when either t - 2 = 0 or t + 1 = 0.

Solving for t, we get:

t = 2 and t = -1

Since time cannot be negative, we discard the -1 solution. Therefore, the brush hits the ground 2 seconds after being thrown.