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In science class, the students were asked to create a container to hold an egg they would then drop this container from a window that is 25 feet above the ground if the equation of the containers pathway can be modelled by the equation: H =-16t²+25Find is the maximum height of the container?

Respuesta :

Answer:

25 feet

Explanation:

The equation that models the pathway of the container is:

[tex]h=-16t^2+25[/tex]

The maximum height occurs at the axis of symmetry.

First, we find the equation of symmetry:

[tex]\begin{gathered} x=-\frac{b}{2a}where\begin{cases}a=-16 \\ b=0\end{cases} \\ x=-\frac{0}{2\times-16} \\ x=0 \\ \implies t=0 \end{gathered}[/tex]

Next, determine the value of h at t=0.

[tex]\begin{gathered} h=-16(0)^2+25 \\ h=25\text{ feet} \end{gathered}[/tex]

The maximum height of the container is 25 feet.