Big Idea 3

Functions can be represented in multiple, equivalent ways.

1 week

Evidence of Understanding

  • create a table of values or graph from an explicit or recursive rule and use it to solve problems
    • graph a parabola from the factored, standard, or vertex form of its equation and label its vertex and intercepts (approximately for non-integer values)
      • strategically use technology to determine the scale and orientation of a parabola in the coordinate plane
    • create a table of values that highlights key characteristics of a quadratic function including its vertex, intercepts, and symmetry
    • find and justify domain and range values for a quadratic from its graph, table, and equation
      • Example: evaluate f(x) = 5 by looking at the graph or table, or find f(3) by looking at the graph, table, or by calculating the value using the rule
      • justify whether a given point is on a parabola, given its equation
      • explore and justify why the domain of a quadratic function contains all real numbers
    • describe how the graph of any equation visually represents values that make the equation true
      • describe the solution set of a quadratic function from its graph


  • construct an explicit or recursive function rule from an equivalent representation
    • describe how quantities from a situation, sequence, or table, or points on a graph map to parts of the factored, standard, or vertex form of a quadratic equation
      • explain why both representations are equivalent
      • describe advantages and disadvantages of different representations for a function
    • create and justify a quadratic equation in factored, standard, or vertex form given a situation, sequence, table or graph
      • Example: create f(x) = (x - 1)2 or f(x) = x2 + 3 and describe the relationship between quantities in the function rule with the situation, table, sequence, or graph that it models
      • use the rate of change to create and justify a recursive rule for a quadratic function


*NOTE:  algebraic conversion between forms of a quadratic equation is part of Unit 6


Develop conceptual understanding:

parent function, transformation, reflection, translation, dilation

Supporting terms to communicate:

function, quadratic, parabola, domain, range, independent, dependent, input, output, axis of symmetry, vertex, maximum, minimum,  root, intercept, rate of change, interval, vertex form, coefficient

Core Resource

A core resource supports multiple days of instruction.

Instructional Routine: Contemplate then Calculate
These tasks are embedded within the instructional routine called Contemplate then Calculate. COMING SOON!