## Related questions with answers

Sean and Mason run out of gas while fishing from their boat in the bay. They set off an emergency flare with an initial vertical velocity of 30 meters per second. The height of the flare in meters can be modeled by $h(t)=-5 t^2+30 t$, where t represents the number of seconds after launch.

Sean wants to know how high the flare will reach above the surface of the water.

a. Write the function in vertex form, factoring so the coefficient of $t^2$ is 1 .

b. Complete the square using the vertex form of the function.

c. How high will the flare reach?

Solution

Verified**(a)** Factor out the given equation by $-5$ to eqaul the coefficient of $t^2$ to $1$:

$\begin{aligned} h(t)&=-5t^2+30t \hspace{3.3cm}\footnotesize{\textcolor{#008ECC}{\text{Factor out by }-5}}\\ h(t)&=-5(t^2{-6}t) \end{aligned}$

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