Algebra 1 Notes - Poudre School District · 2017. 4. 20. · A1S84NotesGraphingF=a(xh)2k.notebook 1...
Transcript of Algebra 1 Notes - Poudre School District · 2017. 4. 20. · A1S84NotesGraphingF=a(xh)2k.notebook 1...
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A1S84NotesGraphingF=a(xh)2k.notebook
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April 20, 2017
Oct 128:01 AM
Algebra 1 Notes
P41 84 Graphing f(x) = a(xh)2 + k
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Oct 87:09 AM
Vertex Formy = a (x h)2 + k
h is a horizontal shift / k is a vertical shiftVertex is at (h, k)Axis (Line) of Symmetry is at x = h
y = 3(x 2)2 + 5
h shifts it to the Right 2.k shifts it Up 5.a means it is stretched.
Vertex is at (2, 5)Line of Symm is at x = 2
a is up/down and stretch/shrink
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Oct 98:58 AM
h is 1 because the formula is (x h)y = 2(x + 1)2 4
h shifts it to the left 1.k shifts it down 4.a means it is stretched.Line of Symm is at x = 1Vertex is at (1, 4)
Using Vertex Form to Graph
Find another point and reflect it over Line of Symm.x = 0y = ? 2
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Oct 87:09 AM
Practice Graphing Vertex Form
y = 3(x + 2)2 + 4
a = Opens Down/Stretchedh = 2k = 4Line of Symm is x = 2Vertex is at (2, 4)
Substitute and Find 1 extra point.Sketch the ParabolaFind another point and reflect it over Line of Symm.x = 0y = ? 8
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Oct 88:35 AM
Converting to Vertex Formy = 2x2 + 8x + 7
1. Find Vertex2. Substitute a, h, and k into the formula
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April 20, 2017
Feb 261:52 PM
Convert from Vertex to Standard
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Example 5
Water fountains are usually designed to give a specific visual effect. For example, the water fountain shown consists of streams of water that are shaped like parabolas. Notice how the streams are designed to land on the underwater spotlights. Write and graph a quadratic function that models the path of a stream of water with a maximum height of 5 feet, represented by a vertex of (3, 5), landing on a spotlight 6 feet from the water jet, represented by (6, 0).
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HW #4984 P446 #2325,3139,41
Please put your name and class period at the top of the homework.Also include the homework number.
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Core Concept
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Example 2
Graph g(x) = (x − 4)2. Compare the graph to the graph of f(x) = x2.
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Monitoring Progress 45
Graph the function. Compare the graph to the graph of f(x) = x2.g(x) = 2(x + 5)2 h(x) = −(x − 2)2
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Example 3
Graph g(x) = −2(x + 2)2 + 3. Compare it to f(x) = x2.
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Monitoring Progress 68
Graph the function. Compare the graph to the graph of f(x) = x2.g(x) = 3(x − 1)2 + 6 h(x) = (x + 4)2 − 2
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Core Concept
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Nov 48:16 AM
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Nov 48:17 AM
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Example 1
Determine whether each function is even, odd, or neither.
a. f(x) = 2x b. g(x) = x2 − 2 c. h(x) = 2x2 + x − 2
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Quadratic Functions
Parent Function y = x2
Reflection in xaxis y = x2