Domain and Range of Quadratic Functions

​1-minute exercise: Balance Poses

https://www.youtube.com/watch?v=LtZxKfqMLqk​

​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.

Multiple Choice

True or False.

The domain of the function whose graph appears at the right is the set of all real numbers.

• True

• False

Multiple Choice

What is the range of the given parabola?

Multiple Choice

What is the range of the given parabola?

• True

• False

Multiple Choice

What is the domain and range of the given parabola?

​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:

Multiple Choice

What is the domain of f(x) = -4x² + 5x - 9?

Multiple Choice

What is the range of f(x) = -x² - 3x + 18?

​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