Chapter 10 Sec 1Chapter 10 Sec 1

Graphing Quadratic Graphing Quadratic FunctionsFunctions

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Algebra 1 Chapter 10 Sections 1

1.1. Find Find a = , b = , ca = , b = , c = . = .

2.2. Find Find y intercepty intercept = (0, = (0, c c).).

3.3. Find Axis of SymmetryFind Axis of Symmetry

4.4. Find Vertex ( AOS , __ ) Find Vertex ( AOS , __ )

Plug Plug AOSAOS in function to find in function to find y.y.

5.5. Look at Look at aa is it (+) min or (-) maxis it (+) min or (-) max

6.6. Find Value Max/Min (Find Value Max/Min (yy of vertex). of vertex).

7.7. Make Table of Values and Plot put Make Table of Values and Plot put vertexvertex in the in the center of the table and graph.center of the table and graph.

The seven steps to graphing.The seven steps to graphing. ff((xx)) = ax = ax22 +bx + c +bx + c

a

bx

2

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Algebra 1 Chapter 10 Sections 1

Quadratic Function Quadratic Function

A A quadratic function quadratic function is described by an is described by an equation of the following form.equation of the following form.

cbxaxxf 2

Linear termLinear term

Quadratic termQuadratic term Constant termConstant term

The graph of any quadratic function is called a The graph of any quadratic function is called a parabolaparabola....

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Algebra 1 Chapter 10 Sections 1

Graph of ParabolaGraph of Parabola

Similar to Pg 526

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Algebra 1 Chapter 10 Sections 1

Max and Min ValuesMax and Min Values

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Algebra 1 Chapter 10 Sections 1

Axis of Symmetry and Axis of Symmetry and y y - intercept- intercept

Find the Find the yy-intercept, the equation of the axis of -intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then symmetry, the vertex , Max or min and Value, then graph. graph. ff((xx) = ) = xx22 + 9 + 8 + 9 + 8xx

Step 1: Arrange terms. Then identify Step 1: Arrange terms. Then identify a, b, and c a, b, and c ff((xx) = ) = xx22 + 9 + 8 + 9 + 8xxff((xx) = ) = xx22 + 8 + 8x +x + 9 9

So So aa = 1, = 1, bb = 8, and = 8, and cc = 9 = 9

Step 2: Find the Step 2: Find the yy-intercept, (0, c) -intercept, (0, c) The The yy-intercept is (0, 9).-intercept is (0, 9).

Step 3: Find the Axis of Symmetry (AOS)Step 3: Find the Axis of Symmetry (AOS)

x b

2a

x 8

2 1 4 AOS = -4AOS = -4

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Algebra 1 Chapter 10 Sections 1

Vertex and GraphVertex and Graph

Find the Find the yy-intercept, the equation of the axis of -intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then symmetry, the vertex , Max or min and Value, then graph. graph. ff((xx) = ) = xx22 + 8 + 8x x + 9+ 9

Step 4: Find the coordinates of the vertex. (AOS, ___). Step 4: Find the coordinates of the vertex. (AOS, ___). Plug AOS in original function to find Plug AOS in original function to find y - y - coordinatecoordinateff(-4) = (-4) = xx22 + 8 + 8x +x + 9 9 = (-4)= (-4)22 + 8(-4) + 9 = 16 - 32 + 9 = -7 + 8(-4) + 9 = 16 - 32 + 9 = -7

Step 5: Max or Min Step 5: Max or Min aa = 1, positive so Minimum = 1, positive so MinimumStep 6: Value of Max/Min: Step 6: Value of Max/Min:

(-4, -7)(-4, -7)vertexvertex

––7 7

Min: –7 Min: –7

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Algebra 1 Chapter 10 Sections 1

xx xx22 + 8 + 8x + x + 99 ff((xx)) ((x,x, ff((xx))

-6-6

-5-5

-4-4

-3-3

-2-2

Vertex and GraphVertex and Graph

Find the Find the yy-intercept, the equation of the axis of -intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then symmetry, the vertex , Max or min and Value, then graph. graph. ff((xx) = ) = xx22 + 8 + 8x + x + 99

xx xx22 + 8 + 8x + x + 99 ff((xx)) ((x,x, ff((xx))

-6-6 (-6)(-6)22 + 8(-6) + 9 + 8(-6) + 9 -3-3 (-6, -3)(-6, -3)

-5-5 (-5)(-5)22 + 8(-5) + 9 + 8(-5) + 9 -6-6 (-5, -6)(-5, -6)

-4-4 (-4)(-4)22 + 8(-4) + 9 + 8(-4) + 9 -7-7 (-4, -7)(-4, -7)

-3-3 (-3)(-3)22 + 8(-3) + 9 + 8(-3) + 9 -6-6 (-3, -6)(-3, -6)

-2-2 (-2)(-2)22 + 8(-2) + 9 + 8(-2) + 9 -3-3 (-2, -3)(-2, -3)

vertexvertex

(-4, -7)(-4, -7)vertexvertex

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Algebra 1 Chapter 10 Sections 1

Graph Graph f(x) = xf(x) = x22 + 8x + 9 + 8x + 9

((x,x, ff((xx))

(-6, -3)(-6, -3)

(-5, -6)(-5, -6)

(-4, -7)(-4, -7)

(-3, -6)(-3, -6)

(-2, -3)(-2, -3)

AOS AOS x x = -4= -4

x x = -4= -4yy-intercept -intercept

(0, 9)(0, 9)

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Algebra 1 Chapter 10 Sections 1

Find Max or MinFind Max or MinConsider the function Consider the function ff((xx) = ) = xx22 - 4 - 4xx + 9 + 9

To find Max/Min without graphing do Steps 1 – 6.To find Max/Min without graphing do Steps 1 – 6.

Step 1. Step 1. aa = 1, = 1, bb = = – – 4, and 4, and cc = 9 = 9

Step 2. Step 2. yy–intercept (0, 9)–intercept (0, 9)

Step 3.Step 3.

Step 4. Find Vertex (2, __)Step 4. Find Vertex (2, __)

ff(2) = (2)(2) = (2)22 - 4(2) + 9 = 4 - 8 + 9 = 5 - 4(2) + 9 = 4 - 8 + 9 = 5

Step 5. Max/Min? Step 5. Max/Min? aa = 1. = 1. a a is positive minimum value.is positive minimum value.

Step 6. Value of Max/Min. The Vertex is (2, 5) So theStep 6. Value of Max/Min. The Vertex is (2, 5) So the

Min value is 5Min value is 5..

AOS b2a

4 2(1)

2 2

55

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Algebra 1 Chapter 10 Sections 1

1.1. Find Find a = , b = , ca = , b = , c = . = .

2.2. Find Find y intercepty intercept = (0, = (0, c c).).

3.3. Find Axis of SymmetryFind Axis of Symmetry

4.4. Find Vertex ( AOS , __ ) Find Vertex ( AOS , __ )

Plug Plug AOSAOS in function to find in function to find y.y.

5.5. Look at Look at a a is it (+)min or (-)maxis it (+)min or (-)max

6.6. Find Value Max/Min (Find Value Max/Min (yy of vertex). of vertex).

7.7. Make Table of Values and Plot put Make Table of Values and Plot put vertexvertex in the in the center of the table and graph.center of the table and graph.

The seven steps to graphing.The seven steps to graphing. ff((xx)) = ax = ax22 +bx + c +bx + c

a

bx

2

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Algebra 1 Chapter 10 Sections 1

Daily AssignmentDaily Assignment

• Chapter 10 Section 1Chapter 10 Section 1• Study Guide (SG)Study Guide (SG)

• Pg 131 - 132 AllPg 131 - 132 All