Standards Map

Mathematics > Course Model Algebra I (Traditional Pathway) > Reasoning with Equations and Inequalities
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Mathematics | Course : Model Algebra I (Traditional Pathway)

Domain - Reasoning with Equations and Inequalities

Cluster - Solve equations and inequalities in one variable.

[AI.A-REI.B.4.a] - Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.

Resources:


  • Quadratic equation
    An equation that includes only second degree polynomials. Some examples are y = 3x2 – 5x2 + 1, x2 + 5xy + y2 = 1, and 1.6a2 +5.9a – 3.14 = 0.

Predecessor Standards:

  • 8.EE.A.2
    Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • AI.A-SSE.B.3.b
    Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • AI.A-REI.A.1
    Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify or refute a solution method.
  • AI.A-REI.B.4.b
    Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the solutions of a quadratic equation results in non-real solutions and write them as a ± bi for real numbers a and b.
  • GEO.G-GPE.A.1
    Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.