Chapter 9: Q3. (page 597)

Consider $y = x^{2} - 7 x + 6$ . Determine whether the function has a maximum or minimum value.

Short Answer

Expert verified

The function $y = x^{2} - 7 x + 6$ hasa minimum value.

Step by step solution

Step 1. Define the concept.

In a quadratic equation $y = a x^{2} + b x + c$ , if the coefficient of $x^{2}$ is positive, then the graph of the parabola is upward open and vertex is at the minimum and if the coefficient of width="17">x2is negative, then the graph of the parabola is downward open and vertex is at maximum.

Step 2. Graphical representation of the quadratic function.

The graph of any quadratic function is a parabola.

$y = a x^{2} + b x + c$ (a is positive) – minimum

$y = a x^{2} + b x + c$ (a is negative) – maximum

Step 3. State whether the function has a maximum or minimum value.

The function $y = x^{2} - 7 x + 6$ , the coefficient of $x^{2}$ is positive; it is upward open, so it has a minimum value.

Therefore, the function $y = x^{2} - 7 x + 6$ has a minimum value.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Consider $y = x^{2} - 7 x + 6$ . Determine whether the function has a maximum or minimum value.

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Graphical representation of the quadratic function.

Step 3. State whether the function has a maximum or minimum value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Statistics

Pure Maths

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Considery=x2−7x+6. Determine whether the function has a maximum or minimum value.

Short Answer

Step by step solution

Step 1. Define the concept.

Step 2. Graphical representation of the quadratic function.

Step 3. State whether the function has a maximum or minimum value.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Statistics

Pure Maths

Mechanics Maths

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Consider $y = x^{2} - 7 x + 6$ . Determine whether the function has a maximum or minimum value.