Big Idea:

Big Idea 2

Equivalent representations of a function highlight different properties.

1 week

Evidence of Understanding

  • identify and justify equivalent representations for a quadratic function
    • describe a quadratic function from the factored, standard, and vertex form of its equation
      • Ex: factored form quickly shows the roots, the average of those roots can determine the axis of symmetry
    • use specific features of a quadratic function to prove representations are equivalent (table, graph, function rule in factored form, standard form, or vertex form)
      • Ex: suppose (3, 9) is the vertex, explain 9 is the y coordinate of the vertex on the graph, 9 is the highest output value in the table and the only output value not repeated
      • Ex: suppose (3, 9) is the vertex, show x = 3 is the axis of symmetry in vertex form and 3 is in the middle of -1 and 7 which are the roots in factored form, etc.
         
  • create equivalent representations for a quadratic function
    • given an equation, use technology to graph a parabola and identify its vertex and intercepts (approximately for non-integer values)
      • justify the scale and orientation of a function’s graph using its intercepts and vertex and can adjust the window of the graphing calculator appropriately
    • without technology, graph a function rule in factored form, standard form, or vertex form
    • use intercepts and/or the vertex from a table or graph to create and justify a function rule in factored form, standard form, or vertex form
    • NOTE:  algebraic conversion between forms of a quadratic equation is part of Unit 6   

Develop conceptual understanding:

factor, factored form, standard form, vertex form

Supporting terms to communicate:

function, quadratic, parabola, y intercept, axis of symmetry, reflection, turning point, maximum, minimum, vertex, x intercept, root, average, domain, range, equivalent

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.