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The height in meters, of a model rocket above the ground is modeled by the function f (t) = -3t^2 + 12t, where t is time in seconds. What is the maximum height the rocket reaches

User Peterino
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1 Answer

3 votes

Answer:

12 meters.

Explanation:

Given the height function of the rocket:
f (t) = -3t^2 + 12t

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
f(x)=ax^2+bc+c, the equation of symmetry is:
x=-(b)/(2a).

In the given function: a=-3, b=12

Equation of symmetry :


t=-(12)/(2*-3)\\t=2.

Step 2: Substitute t=2 into f(t) to solve for the maximum height


f (2) = -3(2)^2 + 12(2)\\=-3*4+24\\=12$ meters

The maximum height reached by the rocket is 12 meters.

User NightFuryLxD
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