1. Chapter 10 Sec 1 Graphing Quadratic Functions

2. 2 of 12 Algebra 1 Chapter 10 Sections 1 1.Find a =, b =, c =. 2.Find y intercept = (0, c). 3.Find Axis of Symmetry 4.Find Vertex ( AOS, __ ) Plug AOS in function to find y. 5.Look at a is it (+) min or (-) max 6.Find Value Max/Min (y of vertex). 7.Make Table of Values and Plot put vertex in the center of the table and graph. The seven steps to graphing. f(x) = ax 2 +bx + c

3. 3 of 12 Algebra 1 Chapter 10 Sections 1 Quadratic Function A quadratic function is described by an equation of the following form. Linear term Quadratic term Constant term The graph of any quadratic function is called a parabola..

4. 4 of 12 Algebra 1 Chapter 10 Sections 1 Graph of Parabola Similar to Pg 526

5. 5 of 12 Algebra 1 Chapter 10 Sections 1 Max and Min Values

6. 6 of 12 Algebra 1 Chapter 10 Sections 1 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) = x 2 + 9 + 8x Step 1: Arrange terms. Then identify a, b, and c f(x) = x 2 + 9 + 8x f(x) = x 2 + 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. 7 of 12 Algebra 1 Chapter 10 Sections 1 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) = x 2 + 8x + 9 Step 4: Find the coordinates of the vertex. (AOS, ___). Plug AOS in original function to find y - coordinate f(-4) = x 2 + 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. 8 of 12 Algebra 1 Chapter 10 Sections 1x x 2 + 8x + 9 f(x)f(x)f(x)f(x) (x, f(x) -6 -5 -4 -3 -2 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) = x 2 + 8x + 9 x x 2 + 8x + 9 f(x)f(x)f(x)f(x) (x, f(x) -6 (-6) 2 + 8(-6) + 9 -3 (-6, -3) -5 (-5) 2 + 8(-5) + 9 -6 (-5, -6) -4 (-4) 2 + 8(-4) + 9 -7 (-4, -7) -3 (-3) 2 + 8(-3) + 9 -6 (-3, -6) -2 (-2) 2 + 8(-2) + 9 -3 (-2, -3) vertex (-4, -7) vertex

9. 9 of 12 Algebra 1 Chapter 10 Sections 1 Graph f(x) = x 2 + 8x + 9 (x, f(x) (-6, -3) (-5, -6) (-4, -7) (-3, -6) (-2, -3) AOS x = -4 y-intercept (0, 9)

10. 10 of 12 Algebra 1 Chapter 10 Sections 1 Find Max or Min Consider the function f(x) = x 2 - 4x + 9 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. Min value is 5. 5

11. 11 of 12 Algebra 1 Chapter 10 Sections 1 1.Find a =, b =, c =. 2.Find y intercept = (0, c). 3.Find Axis of Symmetry 4.Find Vertex ( AOS, __ ) Plug AOS in function to find y. 5.Look at a is it (+)min or (-)max 6.Find Value Max/Min (y of vertex). 7.Make Table of Values and Plot put vertex in the center of the table and graph. The seven steps to graphing. f(x) = ax 2 +bx + c

12. 12 of 12 Algebra 1 Chapter 10 Sections 1 Daily Assignment Chapter 10 Section 1 Study Guide (SG) Pg 131 - 132 All