8.10.7 Lesson Summary

In this lesson, you learned how to:

• Use the factored form of a quadratic expression or a graph of a quadratic function to answer questions about a situation.
• Write equivalent expressions in factored form when given quadratic expressions of the form $a{x}^2+bx+c$ and $a$ is not 1.

Here are the activities that helped you reach those goals:

• 8.10.1: Analyzing Various Quadratic Expressions
  • In this activity, you analyzed different quadratic expressions and found the distinctions that made them unique. Being able to recognize detailed aspects of these expressions helps provide a better understanding that is useful when solving by factoring.
• 8.10.2: Working with Quadratic Factored Form with Leading Coefficient Other Than One
  • In this activity, you learned the process that is involved when attempting to factor a quadratic expression where the leading coefficient is not 1. By using a guess and check method, you were able to solve these expressions.
  • 8.10.2: Self Check
  • 8.10.2: Additional Resources
• 8.10.3: Using Technology to Find Rational Factors
  • In this activity, you applied graphing technology to solve complicated quadratic functions that were not factorable by other means, since the zeros were non-integer rational numbers.
  • 8.10.3: Self Check
  • 8.10.3: Additional Resources
• 8.10.4: Finding the Factors of Quadratic Expressions in Standard Form
  • In this activity, you learned two different methods to factor complicated quadratic equations with leading coefficients greater than 1. You learned to use one method when the leading coefficient was a perfect square and another method when it was not a perfect square.
  • 8.10.4: Self Check
  • 8.10.4: Additional Resources
• 8.10.5: Solving Quadratic Equations by Any Method
  • In this activity, you combined all of the skills you learned in the lesson to factor quadratic equations using any method you preferred.

After these activities, you completed the following practice:

• 8.10.6: Practice