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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.b] - Complete the square in a quadratic expression to reveal the maximum or minimum value 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.
  • 8.F.A.3
    Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
  • 8.F.B.4
    Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MI.A-REI.B.3.a
    Solve linear equations and inequalities in one variable involving absolute value.
  • 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.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.