In this lesson, you will work on activities that focus on the coefficient of the linear term, the $b$ in $a{x}^2+bx+c$, and how changes to it affect the graph. You will discover that adding a linear term to the squared term translates the graph in both horizontal and vertical directions. This understanding will show that writing an expression such as $x^2+b$ in factored form can help us reason how to sketch the graph.

When you finish this lesson, you will be able to:

• Explain how the $b$ in $a{x}^2+bx+c$ affects the graph of the equation.
• Match equations given in standard and factored form with their graph.

Here are the activities that will help you reach those goals:

• 7.13.1: Equivalent Expressions
• 7.13.2: The Linear Term in a Quadratic Expression
  • 7.13.2: Self Check
  • 7.13.2: Additional Resources
• 7.13.3: Writing Equations that Represent a Graph
  • 7.13.3: Self Check
  • 7.13.3: Additional Resources
• 7.14.4: Writing Quadratic Equations from Real Solutions
  • 7.14.4: Self Check
  • 7.14.4: Additional Resources
• 7.13.5: Graphing Quadratic Equations

After that, you’ll practice and review.

• 7.13.6: Practice
• 7.13.7: Lesson Summary