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.