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.