NY Next Generation Math AI-F.IF.8

AI-F.IF.8 is a cluster heading. These are the individual standards under it.

• AI-F.IF.8.a

  For a quadratic function, use an algebraic process to find zeros, maxima, minima, and symmetry of the graph, and interpret these in terms of context.

01

What Students Need to Do

Students rewrite Algebra I functions into equivalent forms that reveal useful graph or context features. For quadratics, forms can expose zeros, a maximum or minimum, and symmetry.

02

What Mastery Looks Like

The student selects and creates a form suited to the question, then explains the revealed property. Factoring, completing the square, or another valid algebraic process preserves the function.

03

Common Misconceptions

Students may treat equivalent forms as different functions or rewrite correctly without interpreting the result. They may use a form that hides the requested feature.

04

How to Assess It

Give f(x) equals x squared minus 8x plus 12. Ask for forms that reveal its zeros and vertex, then interpret each feature.

1. 01

   Match expanded, factored, and vertex-form cards for the same quadratic, then label the visible features.

2. 02

   Ask students which equivalent form best answers a question about zeros, symmetry, or an extremum.

3. 03

   Play equivalent-form verification by expanding, factoring, or testing values at stations.

4. 04

   Rewrite a quadratic profit or height model to identify break-even points or a maximum.

• AII-F.IF.9

  Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• AII-F.IF.8

  The Grades 9–12 version of this standard.

• NY-8.F.2

  Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• AII-A.SSE.3

  Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.