Big Idea:

Big Idea 2

All quadratic functions share similar graphs, behaviors, and characteristics.

1 week

Evidence of Understanding

  • compare and describe quadratic functions in relation to their parent function, f(x) = x2
    • describe translations (vertical or horizontal shift), reflections, or dilations from a given table or graph with the parent function
      • Example: “I noticed each y-value is 3 times the parent function y-value.”
      • Example: “It shifted 3 units left from the parent function, it reflected over the x axis, etc.”
    • explain how transformations impact the key characteristics of a quadratic function
      • compare the interceptsvertexaxis of symmetry, and intervals that are increasing, decreasing, positive, or negative for the parent function with another function
    • create a graph, rule, or table of values given a stated transformation and a parent function
      • Example: given f(x) = (x + 3)2 and the table, graph, or stated transformation of g(x), write an equation of g(x) in terms of f(x)  

 

  • analyze characteristics that distinguish a quadratic function from other function families
    • recognize the lead coefficient, degree, and constant in any polynomial function 
      • describe quadratic functions as a subset of polynomial functions with a degree of 2
    • interpret quadratic graphs, tables, and equations written in factored, standard, and vertex form to distinguish characteristics that are consistent for all quadratic functions
      • Example: recognize all quadratics have 0, 1, or 2 x-intercepts and exactly 1 y-intercept
      • describe how the vertex, axis of symmetry, and zeros for all quadratics are related
      • connect the factors of any polynomial function with the x intercepts on its graph
    • identify the zeroes from factored form, the vertex and axis of symmetry from vertex form, and the y-intercept from standard form of a quadratic function
      • strategically use a graphing calculator to explore and describe characteristics
    • differentiate characteristics for quadratic functions each represented in different way
      • compare quadratic functions using their vertexes and intercepts 

 

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.