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Mathematics > Course Model Mathematics II (Integrated Pathway) > Seeing Structure in Expressions
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - Seeing Structure in Expressions

Cluster - Write quadratic and exponential expressions in equivalent forms to solve problems.

[MII.A-SSE.B.3.a] - Factor a quadratic expression to reveal the zeros of the function it defines.

Resources:


  • Function
    A mathematical relation for which each element of the domain corresponds to exactly one element of the range.
  • Quadratic expression
    An expression that contains the square of the variable, but no higher power of it.

Predecessor Standards:

  • 7.EE.A.1
    Apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. For example, 4x + 2 = 2(2x +1) and -3(x – 5/3) = -3x + 5.
  • 7.EE.A.2
    Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.” A shirt at a clothing store is on sale for 20% off the regular price, “p”. The discount can be expressed as 0.2p. The new price for the shirt can be expressed as p – 0.2p or 0.8p.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.A-SSE.A.2
    Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)2 – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2) – 3).
  • 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.F-IF.C.8.a
    Use the process of factoring and completing the square in a quadratic function to show zeros, minimum/maximum values, and symmetry of the graph and interpret these in terms of a context.
  • MIII.A-APR.B.2
    Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).