Access Point #: MAFS.912.A-REI.2.AP.4aArchived Access Point

loading spinner
Export Print
Solve quadratic equations by completing the square.
Clarifications:

Essential Understandings

Concrete:

  • Count the number of terms in a quadratic equation.
  • Identify the numbers in the equation that would be used to complete the square.
  • Multiply and divide numbers using appropriate tools.
  • Use appropriate tools to calculate squares and square roots.
  • Order the steps for solving an equation using completing the square.
  • Perform operations on fractions.
  • Simplify fractions.
Representation:
  • Simplify radicals.
  • Calculate using multiple operations.
  • Substitute numbers from the equation into a template for completing the square.
  • Calculate squares and square roots using appropriate tools.
  • Determine the root from adding the terms.
  • Determine the root from subtracting the terms.
  • Understand the following vocabulary and concepts: + symbol, factor, coefficient, terms, exponent, base, constant, variable, binomial, monomial, polynomial, square, square root.
  • Move the constants to the same side of the equation.
  • Take half the middle term, square it, and add to both sides of equal sign.
  • Factor the left side into a perfect square.
  • Take the square root of both sides.
  • Solve for x.
    For example:
    begin mathsize 12px style x squared space plus space 6 x space minus space 16 space equals space 0 end style

    begin mathsize 12px style x squared space plus space 6 x space equals space 16 end style

    begin mathsize 12px style x squared space plus space 6 x space plus space 9 space equals space 16 space plus space 9 end style

    begin mathsize 12px style x squared space plus space 6 x space plus 9 space equals space 25 end style

    begin mathsize 12px style open parentheses x space plus 3 close parentheses squared space equals space 25 end style

    begin mathsize 12px style square root of left parenthesis x space plus space 3 right parenthesis squared end root space equals space square root of 25 end style

    begin mathsize 12px style x space plus space 3 space equals space plus-or-minus 5 end style

    begin mathsize 12px style x space equals space minus 5 space minus space 3 comma space x space equals space 5 space minus space 3 end style

    begin mathsize 12px style x space equals space minus 8 comma space 2 end style

     

General Information
Number: MAFS.912.A-REI.2.AP.4a
Category: Access Points
Date Adopted or Revised: 07/14
Cluster: Solve equations and inequalities in one variable. (Algebra 1 - Major Cluster) (Algebra 2 - Supporting Cluster) : 

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Related Standards

This access point is an alternate version of the following benchmark(s).

Related Courses

This access point is part of these courses.
1200310: Algebra 1
1200320: Algebra 1 Honors
1200330: Algebra 2
1200340: Algebra 2 Honors
1200380: Algebra 1-B
1200400: Foundational Skills in Mathematics 9-12
1207310: Liberal Arts Mathematics
1206330: Analytic Geometry
1200410: Mathematics for College Success
1200700: Mathematics for College Algebra
7912090: Access Algebra 1B
1200315: Algebra 1 for Credit Recovery
1200335: Algebra 2 for Credit Recovery
1200385: Algebra 1-B for Credit Recovery
2104350: Engaged Citizenship through Service-Learning 1
2104360: Engaged Citizenship through Service-Learning 2
7912075: Access Algebra 1
7912095: Access Algebra 2

Related Resources

Vetted resources educators can use to teach the concepts and skills in this access point.

Student Resources

Vetted resources students can use to learn the concepts and skills in this access point.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this access point.