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A toy rocket is launched from a platform that is 48 feet high. The rocket's height above the ground is modeled by [tex]h = -16t^2 + 32t + 48[/tex].

Answer :

The maximum height of the rocket is 64 feet.

To find the maximum height of the rocket, we need to find the vertex of the quadratic function [tex]h(t) = -16t^2 + 32t + 48[/tex].

The vertex of a quadratic function [tex]ax^2 + bx + c[/tex] is given by the formula:

[tex]\[ \text{Vertex}(x) = \left( \frac{-b}{2a}, f\left(\frac{-b}{2a}\right) \right) \][/tex]

For our function [tex]h(t) = -16t^2 + 32t + 48[/tex], [tex]a = -16[/tex] and [tex]b = 32[/tex].

So, the t-coordinate of the vertex is:

[tex]\[ t = \frac{-b}{2a} = \frac{-32}{2(-16)} = \frac{-32}{-32} = 1 \][/tex]

Now, we can find the corresponding h-coordinate by plugging t = 1 into the function:

[tex]\[ h(1) = -16(1)^2 + 32(1) + 48 = -16 + 32 + 48 = 64 \][/tex]

So, the maximum height of the rocket is 64 feet.

The complete question is:
A toy rocket is launched from a platform that is 48 feet high. The rocket's height above the ground is modeled by [tex]h(t) = -16t^2 + 32t + 48[/tex]. Find the maximum height of the rocket.

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