Standards Map

Mathematics > Course Model Mathematics II (Integrated Pathway) > Reasoning with Equations and Inequalities
Accessibility Mode: Note: You are viewing this information in accessibility mode. To view the map, enlarge your window or use a larger device.

Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Reasoning with Equations and Inequalities

Cluster - Solve equations and inequalities in one variable.

[MII.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:

  • MI.A-REI.A.1
    Explain each step in solving a simple linear 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.
  • MII.A-SSE.B.3.b
    Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
  • MII.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 quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
  • MII.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.