​Domain and Range of Quadratic Functions

​Objectives:

​1. Graph quadratic functions.

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2. Define and illustrate domain and range.

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3. Find the domain and range of quadratic functions given:

(a) graph

(b) equation​

​Steps in Graphing Quadratic Functions

​1. Determine the vertex (h, k)

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2. Find the axis of symmetry.

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3. Find other points on the parabola.

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4. Graph the parabola.​

​Example 1: Sketch the graph of f(x) = x².

​https://www.geogebra.org/graphing?lang=en

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https://www.desmos.com/calculator

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​Example 2: Sketch the graph of f(x) = (x + 3)².

​https://www.geogebra.org/graphing?lang=en

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https://www.desmos.com/calculator

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​Example 3: Sketch the graph of f(x) = -x² - 4x

​https://www.geogebra.org/graphing?lang=en

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https://www.desmos.com/calculator

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​Bring the following:

​2 sheets of graphing paper

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pencil

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ruler​

​One Minute Exercise : Harmony Claps

https://www.youtube.com/watch?v=06z3HyVC1-w​

​Example 4: Find the domain and range of the function graphed below.

​Example 5: Find the domain and range of the function graphed below.

​Example 6: Find the domain and range of the function graphed below.

​Example 7: Find the domain and range of the function graphed below.

​Domain of f(x) = ax² + bx + c

​-is the set of all real numbers.

Notation:​

​read as "for all x such that (s.t.) x is an element of real numbers"

​Range of f(x) = ax² + bx + c

​need to know the following:

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​1. opening of parabola

​2. y-coordinate of the vertex of the parabola

​Example 8: Find the domain and range of f(x) = x² + 8x + 12

​Solution:

Domain:​

​Range:

​Example 8: Find the domain and range of f(x) = x² + 8x + 12

​Alternative Solution:

Domain:​

​Range:

​Example 9: Find the domain and range of f(x) = -2x² - 12x - 16

​Solution:

Domain:​

​Range:

​Example 9: Find the domain and range of f(x) = -2x² - 12x - 16

​Alternative Solution:

Domain:​

​Range:

​Activity 1: Sketch the graph of the following functions on clean sheets of graphing paper.

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1) f(x) = -(x - 7)² + 9

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2)​ f(x) = x² - 4x - 6

​Format:

​Online Reference:

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​https://www.onlinemath4all.com/domain-and-range-of-a-quadratic-function.html