WARM UP – noncalculator€¦ · September 25, 2015 Sep 258:17 AM Homework Answers Section 3.6 Sep...
Transcript of WARM UP – noncalculator€¦ · September 25, 2015 Sep 258:17 AM Homework Answers Section 3.6 Sep...
5.1 Quadratic Functions.notebook
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Sep 258:17 AM
Homework Answers Section 3.6
Sep 2510:31 AM
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WARM UP – noncalculator1) Multiply: (2x 5)(x + 3)
2) What two numbers have a product of 24 and a sum of 5?
3) You may use your calculator to answer: What is the lowest point (vertex) of y = 5x2 10x 1
8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
87654321
12345678
x
y
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5.1 Quadratic Equations and FunctionsStandard Form of Quadratic Function
f(x) = ax 2 + bx + c (when a = 0)Parent Function f(x) = x2
Graph is a parabola
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Where do we see parabolas in the real world?
Oct 58:34 AM
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Classifying FunctionsDetermine whether each function is linear or quadratic. Identify the value of a, b, c in each problem.
1) y = (2x – 5)(x + 3)
2) y = 6(x2 – 4x) – 2(3x2 + 7x)
3) f(x) = x2 – (x + 1)(x – 1)
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Vocabularyf(x) = ax2 + bx + c
VertexMinimum point(when a > 0)orMaximum point(when a < 0)
Axis of Symmetry is the line that divides a parabola into two parts that are mirror images.
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8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
87654321
12345678
x
y
8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
87654321
12345678
x
y
ExamplesIdentify the vertex and axis of symmetry of each graph.
Vertex ( ___, ___ )Vertex ( ___, ___ )Axis of Symmetry Axis of Symmetry
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ACT and CSAP PRACTICE PROBLEMS
6. For the function h(x) = 4x2 – 5x, what is the value of h(3)?
A. 93B. 9C. 21
E. 159ACT59F #19
D. 51
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7. The equation for the curve in Figure 1 is y = x2. Which of the following equations BEST represents the curve shown in Figure 2?
Figure 1 Figure 2
A. y = x2/3 B. y = 3x2C. y = x2 + 5 D. y = x2 – 5
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8) Which function is not quadratic?
A. y = 7x – 3x2
C. y = 6x2+ x
D. y = (x + 5)(x – 6)
B. f(x) = 3x – x2 + 8 + x2
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ASSIGNMENT 5.1
p. 241 #115 (Identify a,b,c for 19),
#44 47, and #50 (just solve using elimiation)
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Homework: page 241
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Solve # 50 using elimination: