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Mathematics > Course Model Mathematics II (Integrated Pathway) > Reasoning with Equations and Inequalities
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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.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.

Resources:


  • Complex number
    A number that can be written as the sum or difference of a real number and an imaginary number.
  • 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.
  • Real number
    A number from the set of numbers consisting of all rational and all irrational numbers.

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-CED.A.1
    Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and exponential functions with integer exponents.*
  • 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.N-CN.C.7
    Solve quadratic equations with real coefficients that have complex solutions.
  • MII.A-SSE.B.3.a
    Factor a quadratic expression to reveal the zeros of the function it defines.
  • 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.
  • MII.A-REI.C.7
    Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
  • MIII.N-CN.C.9
    (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
  • PC.N-CN.C.9
    (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.