Question

If the equation is h= -2x^2 + 12x -10 how do I find the max height?

Answer 1

One other way to solve this question is finding the derivative

$h=-2x^2+12x-10$

$h'=-4x+12$

now we have to find when this function will be zero

$-4x+12=0$

$\boxed{\boxed{x=3}}$

now we just replace this value at our initial function

$h=-2x^2+12x-10$

$h_{max}=-2*(3)^2+12*3-10$

$h_{max}=-18+36-10$

$\boxed{\boxed{h_{max}=8}}$

Answer 2

The maximum height is the ordinate value of the vertex of the parabola, ie: yV

Calculating yV:

$y_V=\frac{-\Delta}{4a}\\ \\ y_V=-[\frac{12^2-4*(-2)*(-10)]}{4*(-2)}=\frac{-(144-80)}{-8}=\frac{-64}{-8}=8$