Determine whether the given function has a maximum or a minimum value. Then, find the maximum or minimum value of the function. f (x) = - 2x^2 + 10x + 6

a. The function has a minimum value. The minimum value of the function is - 31.5.

b. The function has a maximum value. The maximum value of the function is 18.5.

c. The function has a maximum value. The maximum value of the function is - 31.5.

d. The function has a minimum value. The minimum value of the function is 18.5.

b. The function has a maximum value. The maximum value of the function is 18.5.

Step-by-step explanation:

Let's consider the equation of a parabola.

f (x) = - 2x² + 10x + 6

where,

a: - 2

b: 10

c: + 6

The sign of "a" determines the openness of the parabola. Since a < 0, the parabola is open downwards and has a maximum.

We can find "x" of the vertex using the following expression.

x (v) = - b/2a = - 10/2. (-2) = - 2.5

We can find the "y" of the vertex by replacing this x in the equation

y (v) = - 2. (2.5) ² + 10. (2.5) + 6 = 18.5

The vertex (maximum) is (2.5, 18.5).