# find the values of b such that the function has the given maximum or minimum value.f(x) = -x^2+bx-75,Maximum value: 25

find the values of b such that the function has the given maximum or minimum value. $f\left(x\right)=-{x}^{2}+bx-75$, Maximum value: 25

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mhalmantus

1.Write the equation in standard form.

$f\left(x\right)=-{x}^{2}+bx-75$

$=-\left({x}^{2}-bx\right)-75$

$=-\left({x}^{2}-bx+\left({b}^{\frac{2}{4}}\right)-\left({b}^{\frac{2}{4}}\right)\right)-75$

$=-{\left(x-\frac{b}{2}\right)}^{2}-75+{b}^{\frac{2}{4}}$

2.Use the maximum to find b.

$-75+{b}^{\frac{2}{4}}=25{b}^{\frac{2}{4}}=100{b}^{2}=400b=±20$