Find the rocks greatest height

[Anna55]

Peter is standing on a cliff by the sea, and drops a rock that falls towards the sea. After t seconds the rock's height over the water, h (t) meters, can be described by the quadric function h (t)=8.5+9.8t-4.9^2
Find the rocks greatest height with respect to the sea level.

When zero seconds have passed Peter is holding the stone. Therefore plugged in 0 instead of t and rearranged the function.
-4.9(0)^2+9.8(0)+8.5=height
0+0+8.5=height
8.5 m=height
However this answer is incorrect and the correct answer should be 13 m. How should I solve it? Thank you in advance!

 

[galactus]

Differentiate your quadratic, set to 0 and solve for t.

Plug that value into the quadratic and you should get your height.

You can also solve it without calculus by using \(\displaystyle t=\frac{-b}{2a}\)

It would appear the rock was not merely dropped straight down, but tossed in the air.

This would form the parabola.

Graph the quadratic and you can see the rocks path.

Remember, if you graph it, do not use t as the variable. Use x.

 

[Anna55]

Thank you I understand how to solve it now!