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### 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.
Students analyze different representations of quadratic functions to determine what characteristics of quadratic functions are true for every quadratic function, and then extend their understanding to analyze polynomial functions.
Resource: