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Chapter 6 Sec 1

Chapter 6 Sec 1. Graphing Quadratic Functions. The seven steps to graphing. f ( x ) = ax 2 + bx + c. Find a = , b = , c = . Find y intercept = (0, c ). Find Axis of Symmetry Find Vertex ( AOS , __ ) Plug AOS in function to find y. Look at a is it (+)min or (-)max

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Chapter 6 Sec 1

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  1. Chapter 6 Sec 1 Graphing Quadratic Functions

  2. The seven steps to graphing.f(x) = ax2 +bx + c • Find a = , b = , c = . • Find y intercept = (0, c). • Find Axis of Symmetry • Find Vertex ( AOS , __ ) • Plug AOS in function to find y. • Look at a is it (+)min or (-)max • Find Value Max/Min (y of vertex). • Make Table of Values and Plot put vertex in the center of the table and graph.

  3. Quadratic Function A quadratic function is described by an equation of the following form. Linear term Constant term Quadratic term The graph of any quadratic function is called a parabola..

  4. Graph of Parabola

  5. Max and Min Values

  6. Axis of Symmetry and y - intercept Find the y-intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then graph. f(x) = x2 + 9 + 8x Step 1: Arrange terms. Then identify a, b, and c f(x) = x2 + 9 + 8x f(x) = x2 + 8x + 9 So a = 1, b = 8, and c = 9 Step 2: Find the y-intercept, (0, c) The y-intercept is (0, 9). Step 3: Find the Axis of Symmetry (AOS) AOS = -4

  7. Vertex and Graph Find the y-intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then graph. f(x) = x2 + 8x + 9 Step 4: Find the coordinates of the vertex. (AOS, ___). Plug AOS in original function to find y - coordinate f(-4) = x2 + 8x + 9 = (-4)2 + 8(-4) + 9 = 16 - 32 + 9 = -7 Step 5: Max or Min a = 1, positive so Minimum Step 6: Value of Max/Min: (-4, -7) vertex –7 Min: –7

  8. Vertex and Graph Find the y-intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then graph. f(x) = x2 + 8x + 9 (-4, -7) vertex vertex

  9. Graph Graph f(x) = x2 + 8x + 9 y-intercept (0, 9) x = -4 AOS x = -4

  10. Find Max or Min To find Max/Min without graphing do Steps 1 – 6. Step 1. a = 1, b = – 4, and c = 9 Step 2. y–intercept (0, 9) Step 3. Step 4. Find Vertex (2, __) f(2) = (2)2 - 4(2) + 9 = 4 - 8 + 9 = 5 Step 5. Max/Min? a = 1. a is positive minimum value. Step 6. Value of Max/Min. The Vertex is (2, 5) So the Min value is 5. Consider the function f(x) = x2 – 4x + 9 5

  11. The seven steps to graphing.f(x) = ax2 +bx + c • Find a = , b = , c = . • Find y intercept = (0, c). • Find Axis of Symmetry • Find Vertex ( AOS , __ ) • Plug AOS in function to find y. • Look at a is it (+)min or (-)max • Find Value Max/Min (y of vertex). • Make Table of Values and Plot put vertex in the center of the table and graph.

  12. Daily Assignment • Chapter 6 Section 1 • Skill Practice Workbook (SPW) • Pg 36 All

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