In Exercises 89–92, find the values of b such that the function has the given maximum or minimum

step 1 Okay, so here we are given f -fx equals minus times x squared plus b times x minus 75. Okay, we

In Exercises 89–92, find the values of b such that the...

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Key Concepts

Quadratic Function

A quadratic function is a polynomial function of degree two and can be written in the standard form ax^2 + bx + c. Its graph is a parabola, and understanding its properties such as the axis of symmetry, vertex, and direction of opening (upward if a > 0, downward if a < 0) is essential in analyzing maximum and minimum values.

Vertex Formula

The vertex of a quadratic function provides the point where the maximum or minimum value of the function occurs. It can be found using the formula x = -b/(2a) when the function is in standard form ax^2 + bx + c. This formula is crucial for determining the coordinates of the vertex and, subsequently, the extreme value of the function.

Completing the Square

Completing the square is an algebraic method used to rewrite a quadratic function in vertex form. This form makes it easier to identify the vertex and the maximum or minimum value. The process involves manipulating the quadratic expression into a perfect square plus a constant, thereby directly revealing the function's extreme value.

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