Answer:
The maximum height of the rocket is about 391.1 feet.
Step-by-step explanation:
The height of the rocket y in feet x seconds after launch is modeled by the equation:
[tex]y=-16x^2+125x+147[/tex]
We want to find the maximum height reached by the rocket.
Since this is a quadratic equation, the maximum height occurs at the vertex. The vertex of a quadratic is given by:
[tex]\displaystyle \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -16, b = 125, and c = 147.
Thus, the x-coordinate of our vertex is:
[tex]\displaystyle x=-\frac{125}{2(-16)}=\frac{125}{32}[/tex]
To find the maximum height, we will substitute this value back in. So:
[tex]\displaystyle y_{\text{max}}=-16\left(\frac{125}{35}\right)^2+125\left(\frac{125}{32}\right)+147\approx391.1\text{ feet}[/tex]
The maximum height of the rocket is about 391.1 feet.
