Given the Quadratic function:
[tex]y=-16x^2+216x+6[/tex]
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:
[tex]x=-\frac{b}{2a}[/tex]
Knowing that a Quadratic function has this form:
[tex]y=ax^2+bx+c[/tex]
You can identify that, for this case:
[tex]\begin{gathered} a=-16 \\ b=216 \end{gathered}[/tex]
Substituting values into the formula, you get this result:
[tex]\begin{gathered} x=-\frac{216}{2(-16)} \\ x=6.75 \end{gathered}[/tex]
It took the rocket 6.75 seconds to reach its maximum height; so the answer is the Third option.
