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## Graphing Quadratic Functions

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Write a function that describes a relationship between two quantities.

Using tables, graphs, and verbal descriptions, interpret the key characteristics of a function which models the relationship between two quantities. Sketch a graph showing key features including: intercepts; interval where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

## Modeling with Quadratic Functions

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Write a function that describes a relationship between two quantities.  Create linear, quadratic, and exponential equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

## Modeling with Quadratic Functions

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Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.  Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

## Graphing Quadratic Functions in Vertex Form

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.  Graph linear and quadratic functions and show intercepts, maxima, and minima.

## Quadratic Functions in Intercept Form

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Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Factor a quadratic expression to reveal the zeros of the function it defines.

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.  Graph linear and quadratic functions and show intercepts, maxima, and minima.

## Inverses of Quadratic Functions

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Find inverse functions.  Produce an invertible function from a non-invertible function by restricting the domain.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

## Writing Quadratic Functions in Vertex Form

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Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.