An object is launched at 19.6 m/s from a height of 58.8 m. The equation for the height (h) in terms of time (t) is given by h(t) = -4.9t² +19.6t + 58.8. What is the object's maximum height?

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An object is launched at 19.6 m/s from a height of 58.8 m. The equation for the height (h) in terms of time (t) is given by h(t) = -4.9t² +19.6t + 58.8. What is the object's maximum height?

Mathematics
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There are a couple of ways to solve this, and the method you should use depends on the type of math course you are in. Is this for a calculus course or an algebra course?
It's algebra two, year three in high school.
Ah, okay. Then the way to solve this is to recognize that the equation for the height is going to give you a parabola opening downward. The highest point will be at the vertex of that parabola. Do you know how to find the vertex?

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No.. :|
The x coordinate of the vertex will always be \(\Large \frac{-b}{2a}\). In this case, that will give you the time that the ball is at its highest point. From there, if you want to figure out the height, you can just plug that time into h(t).
Let me know if you have any questions.

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