Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.f(x) = x2 + 2x - 7

The given function is a quadratic function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

The sign of the coefficient a determines whether the function has a maximum or minimum value. If a > 0, the function has a minimum value. If a < 0, the function has a maximum value.

In the given function f(x) = x^2 + 2x - 7, the coefficient a is 1, which is greater than 0. Therefore, the function has a minimum value.

The x-coordinate of the vertex of a parabola given by f(x) = ax^2 + bx + c is -b/2a. Substituting the given values of a and b, we get -b/2a = -2/(2*1) = -1.

Substituting x = -1 in the given function, we get the minimum value of the function as f(-1) = (-1)^2 + 2*(-1) - 7 = 1 - 2 - 7 = -8.

Therefore, the function f(x) = x^2 + 2x - 7 has a minimum value of -8.