Graphing Quadratic Functions Introduction Lesson Assessment.
Table of Contents Graphing Quadratic Functions – Standard Form It is assumed that you have already...
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Transcript of Table of Contents Graphing Quadratic Functions – Standard Form It is assumed that you have already...
Table of Contents
Graphing Quadratic Functions – Standard Form
• It is assumed that you have already viewed the previous slide show titled
Graphing Quadratic Functions – Concept.
• The summary of the Concept slide show is given again on the next page.
Table of Contents
SUMMARY
• Axis of symmetry: -value of vertexxx
Graphs of Quadratic Functions
• The graph of a quadratic function in called a parabola.
• The maximum or minimum y-value of a quadratic occurs at the vertex.
0a Face Up 0a Face Down•
x-int: y = f (x) = 0 and solve for x.
y-int: x = 0 and solve for y.
•
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2( ) ( )f x a x h k
The vertex is given by V(h,k).
• Example 12( ) 3( 2) 4f x x
The vertex is given by: (2,4)V
• A quadratic function in what we will call Standard Form is given by:
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• Example 2
2( ) 2( 3) 5f x x
The vertex is given by: ( 3, 5)V
2( ) ( )f x a x h k
Put the function in the form of …
2( ) 2( ( 3)) ( 5)f x x
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2( ) 2( 3) 5f x x
The vertex is given by: ( 3, 5)V
Here is an easier way to work the last problem:
For the h value, take the opposite sign … For the k value, take
the same sign …
3h 5k
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• Example 3
22( ) ( 5) 7
3f x x
The vertex is given by: ( 5,7)V
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• Recall that the Axis of Symmetry has the equation
Since the vertex of the standard quadratic function given by
( , )V h k
-value of vertexxx
has an x-value of h, we can write the equation of the axis of symmetry as
x h• Put all of the tools learned so far together to sketch the graph of a quadratic function in standard form.
Table of Contents
2( ) ( )f x a x h k
Sketch the Graph of a Quadratic in Standard Form
0a Face Up
0a Face Down
Vertex ( , )V h k
Axis of symmetry
x h
x-int: f (x) = 0 and solve for x
y-int: x = 0 and solve for y
Draw the parabola
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• Example 4
2( ) 2 1f x x
Sketch the graph of the following function:
Face Up1 0a
Vertex: 2, 1V
Axis of Symmetry: 2x
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• Start the sketch of the graph with what we have so far.
2, 1V
4
2
5
4
2
5
4
2
5
Axis of Symmetry
2x
The parabola is face up
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2( ) 2 1f x x
x-intercepts
22 1 0x
22 1x
2 1x 2 1x
1,0 3,0
y-intercept
0x
2(0) 0 2 1f
4 1 3
0,3
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• Plot the intercepts
4
2
5
x-intercepts
1,0
3,0
4
2
5
y-intercept 0,3
4
2
5
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4
2
5
• Sketch the parabola, using the points and axis of symmetry.
4
2
5
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• Example 5
2( ) 2 3 4f x x
Sketch the graph of the following function:
Face Down2 0a
Vertex: 3,4V
Axis of Symmetry: 3x
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• Start the sketch of the graph with what we have so far.
3,4V
Axis of Symmetry
3x
The parabola is face down
4
2
-2
-5
4
2
-2
-5
4
2
-2
-5
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x-intercepts
22 3 4 0x
22 3 4x
23 2x
4.4,0 1.6,0
2( ) 2 3 4f x x
3 2x
3 2x
4.41, 1.59x
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4
2
-2
-5
• Plot the x-intercepts
x-intercepts
4.4,0
1.6,0
4
2
-2
-5
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y-intercept
0x
2(0) 2 0 3 4f
0, 14
2( ) 2 3 4f x x
(0) 2 9 4f (0) 14f
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• Skip plotting the y-intercept since it is off of the graph.
4
2
-2
-5
•Sketch the parabola, using the points and axis of symmetry.
4
2
-2
-5
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