Question

Find the values of $\boldsymbol{b}$ such that the function has the given maximum or minimum value. $$f(x)=-x^{2}+b x-75 ; \text { Maximum value: } 25$$

Name: Problem 89, Chapter 2: Precalculus: A Concise Course
Uploaded: 2021-02-06T21:14:17-08:00
Duration: 1 min 52 s
Channel: Vanessa Lamar
Description: Find the values of b such that the function has the given maximum or minimum value. f(x)=-x^2+b x-75 ; Maximum value: 25

   Find the values of $\boldsymbol{b}$ such that the function has the given maximum or minimum value.
$$f(x)=-x^{2}+b x-75 ; \text { Maximum value: } 25$$

Precalculus: A Concise Course

Ron Larson, Robert… 3rd Edition

Chapter 2, Problem 89

Instant Answer

Solved by Expert Vanessa Lamar

02/06/2021

Step 1

The given function is a quadratic function of the form $ f(x) = -x^2 + bx - 75 $. Since the coefficient of $ x^2 $ is negative, the parabola opens downwards, indicating that the function has a maximum value. Show more…

Show all steps

Thanks for your feedback!

Find the values of $\boldsymbol{b}$ such that the function has the given maximum or minimum value. $$f(x)=-x^{2}+b x-75 ; \text { Maximum value: } 25$$

Play audio

Feedback

Vanessa Lamar and 92 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vertex of a Parabola

The vertex of a parabola is the point at which the function attains its maximum or minimum value. For a quadratic function f(x) = ax² + bx + c, the vertex can be found using the formula x = -b/(2a). The y-coordinate of the vertex is then calculated by substituting this x-value back into the function.

Quadratic Functions

A quadratic function is a second-degree polynomial function of the form f(x) = ax² + bx + c. These functions graph as parabolas, which open upwards if a > 0 and downwards if a < 0. They appear frequently in problems involving optimization, such as finding maximum or minimum values.

Completing the Square

Completing the square is a method used to rewrite a quadratic function in vertex form, which clearly shows the vertex of the parabola. This transformation makes it easier to identify the maximum or minimum value of the function and is particularly useful when solving optimization problems or describing the function's graph.

Please give Ace some feedback