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### 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
• 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.

• Equivalent Representations
During this week students create and study different representations of quadratic functions in order to make connections between the different representations.
Resource:
Equivalent Representations

During this week students create and study different representations of quadratic functions in order to make connections between the different representations.

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