place the option that correctly completes the sentence. for a science project, joseph launches a model…

Answer:

1 second

Explanation:

Step1: Identify the function type

The height function $h(s)=-3s^{2}+6s + 45$ is a quadratic function in the form $y = ax^{2}+bx + c$ where $a=-3$, $b = 6$ and $c = 45$.

Step2: Recall the formula for the vertex - x - coordinate

For a quadratic function $y=ax^{2}+bx + c$, the $x$-coordinate (in our case $s$-coordinate) of the vertex (which gives the time at which the maximum height is reached for a downward - opening parabola, since $a=-3<0$) is given by $s=-\frac{b}{2a}$.

Step3: Substitute the values of a and b

Substitute $a=-3$ and $b = 6$ into the formula $s=-\frac{b}{2a}$. We get $s=-\frac{6}{2\times(-3)}$.

Step4: Simplify the expression

First, calculate the denominator $2\times(-3)=-6$. Then $s =-\frac{6}{-6}=1$. So it will take the rocket 1 second to reach its maximum height.