Question

A model rocket is launched straight up. Its height in feet (y) above theground x seconds after launch is modeled by the quadratic function: y=-16x2 + 216x + 6.How many seconds did it take the rocket to reach its maximum height?

Answer 1

Given the Quadratic function:

`y=-16x^2+216x+6`

You need to find the x-coordinate of the vertex of the parabola, in order to calculate how many seconds it took the rocket to reach its maximum height.

You can find the x-coordinate of the vertex of the parabola with the following formula:

`x=-(b)/(2a)`

Knowing that a Quadratic function has this form:

`y=ax^2+bx+c`

You can identify that, for this case:

`\begin{gathered} a=-16 \\ b=216 \end{gathered}`

Substituting values into the formula, you get this result:

`\begin{gathered} x=-(216)/(2(-16)) \\ x=6.75 \end{gathered}`

It took the rocket 6.75 seconds to reach its maximum height; so the answer is the Third option.