If the equation is [tex]h = -2x^2 + 12x - 10[/tex], how do I find the maximum height?

One other way to solve this question is finding the derivative
h = − 2 x 2 + 12 x − 10
h ′ = − 4 x + 12
now we have to find when this function will be zero
− 4 x + 12 = 0
x = 3 ​ ​
now we just replace this value at our initial function
h = − 2 x 2 + 12 x − 10
h ma x ​ = − 2 ∗ ( 3 ) 2 + 12 ∗ 3 − 10
h ma x ​ = − 18 + 36 − 10
h ma x ​ = 8 ​ ​

Answered by D3xt3R | 2024-06-10

The maximum height is the ordinate value of the vertex of the parabola, ie: yV
Calculating yV:
y V ​ = 4 a − Δ ​ y V ​ = − [ 4 ∗ ( − 2 ) 1 2 2 − 4 ∗ ( − 2 ) ∗ ( − 10 )] ​ = − 8 − ( 144 − 80 ) ​ = − 8 − 64 ​ = 8

Answered by Ryan2 | 2024-06-10

To find the maximum height of the equation h = − 2 x 2 + 12 x − 10 , use the vertex formula x = − 2 a b ​ to find x = 3 . Substitute this back into the equation to obtain the maximum height of h ma x ​ = 8 .
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Answered by D3xt3R | 2024-11-13