Answer:
12 meters.
Step-by-step explanation:
Given the height function of the rocket: [tex]f (t) = -3t^2 + 12t[/tex]
The function is a parabola which opens up and the maximum height is reached at the axis of symmetry.
Step 1: Determine the equation of symmetry
For any quadratic equation of the form [tex]f(x)=ax^2+bc+c[/tex], the equation of symmetry is: [tex]x=-\dfrac{b}{2a}[/tex].
In the given function: a=-3, b=12
Equation of symmetry :
[tex]t=-\dfrac{12}{2*-3}\\t=2[/tex].
Step 2: Substitute t=2 into f(t) to solve for the maximum height
[tex]f (2) = -3(2)^2 + 12(2)\\=-3*4+24\\=12$ meters[/tex]
The maximum height reached by the rocket is 12 meters.
