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What is the maximum value of f(x)=-5x^2+10x+7

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Final answer:

The maximum value of the function f(x) = -5x^2 + 10x + 7 is 12.

Step-by-step explanation:

The maximum value of the function f(x) = -5x^2 + 10x + 7 can be found using the vertex form of a quadratic equation.

In general, a quadratic function of the form f(x) = ax^2 + bx + c has a maximum value at the vertex, where the x-coordinate of the vertex is given by x = -b/2a.

For the given function f(x) = -5x^2 + 10x + 7, the coefficient of x^2 is -5, the coefficient of x is 10, and the constant term is 7.

Plugging these values into the formula x = -b/2a, we get x = -10/(2*(-5)) = 1.

The maximum value can be found by substituting this x-value into the function: f(1) = -5(1)^2 + 10(1) + 7 = 12.

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