Question

Some fireworks are fired vertically into the air from the ground at an initial speed of 80 feet per second. The equation for this object's height h(t) at time t seconds after launch is h(t) = -16t2 + 80t. a. Find the vertex. Explain what this means in the context of the situation

Answer 1

Answer:

Vertex (-2.5,-300)

Step-by-step explanation:

We are given with h(t)=-16 t^2 +80 t.  We are asked to find the vertex.

X-coordinate of vertex =$\frac{-b}{2a}$

Where 'a' is coefficient of $t^{2}$ term

'b' is coefficient of 't' term.

From given function, a= -16

b=80

So,

x-coordinate of vertex =$\frac{-80}{2(-16)}$

                                =-2.5

y-coordinate of vertex =$-16(-2.5)^{2} +80(-2.5)$

Simplify it,

            =-100 -200

           = -300

So, vertex is at (-2.5, -300).