Big Idea:

Big Idea 1

Rate of change determines other characteristics of a quadratic function.

1 week

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

 

  • 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 symmetryzeros, 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
    • 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

 

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

Core Resource

A core resource supports multiple days of instruction.

  • Distinguishing Quadratics
    This Core Resource, when complete, will focus how we can distinguish quadratic functions from linear and exponential functions based on their properties.
    Resource:
    Distinguishing Quadratics

    This Core Resource, when complete, will focus how we can distinguish quadratic functions from linear and exponential functions based on their properties when represented as sequences, tables, graphs, focusing on using rate of change to find intervals of a function that are increasing, decreasing, positive, negative, and symmetry of a function (if any).

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