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

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(2) Answers

alexas89

One other way to solve this question is finding the derivative
[latex]h=-2x^2+12x-10[/latex]
[latex]h'=-4x+12[/latex]
now we have to find when this function will be zero
[latex]-4x+12=0[/latex]
[latex]\boxed{\boxed{x=3}}[/latex]
now we just replace this value at our initial function
[latex]h=-2x^2+12x-10[/latex]
[latex]h_{max}=-2*(3)^2+12*3-10[/latex]
[latex]h_{max}=-18+36-10[/latex]
[latex]\boxed{\boxed{h_{max}=8}}[/latex]

lily5

The maximum height is the ordinate value of the vertex of the parabola, ie: yV
Calculating yV:
[latex]y_V=\frac{-\Delta}{4a}\\ \\ y_V=-[\frac{12^2-4*(-2)*(-10)]}{4*(-2)}=\frac{-(144-80)}{-8}=\frac{-64}{-8}=8[/latex]