Evidence of Understanding

**compare linear, quadratic, and exponential function families using the rate of change**- analyze the rate of change from a graph, table, or sequence to identify input and output values that belong in a
**quadratic function**- identify variables within a situation and describe how they relate to each other

- recognize the second difference for quadratic functions is non-zero constant
- describe how quadratic functions are different from linear and exponential functions
- compare growth rates for linear, exponential, and quadratic functions and recognize that exponential and quadratic functions increase faster than linear functions and that exponential functions eventually exceed quadratic functions

- use the rate of change to justify which function family provides the best model

- analyze the rate of change from a graph, table, or sequence to identify input and output values that belong in a

**use the rate of change to interpret key characteristics of a quadratic function**- identify and interpret the most important characteristics of a quadratic from its graph or table of values and describe what they mean within the context of a situation
- key characteristics include: intervals where the function is increasing, decreasing, positive, or negative, intercepts, maximums or minimums, and symmetries

- describe the
**vertex**in relation to the rate of change,**axis of symmetry**,**zeros**, and**range** - analyze the axis of symmetry and rate of change to predict outputs for a quadratic function
- calculate the
**average rate of change**between two points and recognize that the average rate of change is zero for points that reflect one another across the axis of symmetry - apply patterns relating inputs and outputs to create an equation for the axis of symmetry

- calculate the
- approximate the
**domain**and range of a quadratic function from a situation, graph, or rule- describe restrictions on the domain and range in the context of a situation
- relate restrictions on the range with the vertex of the
**parabola**

- identify and interpret the most important characteristics of a quadratic from its graph or table of values and describe what they mean within the context of a situation

Develop conceptual understanding:

quadratic, parabola, axis of symmetry, vertex, roots

Supporting terms to communicate:

function, rate of change, average rate of change, turning point, maximum, minimum, intercept, interval, increasing, decreasing, positive, negative, domain, range, reflection, average