Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing  DESCRIBE the Elements of the GRAPH of a Quadratic Equation  DETERMINE a Standard Approach to GRAPHING A Quadratic Equation  Use a GRAPHING CALCULATOR to Graph a Quadratic Equation  SOLVE a Quadratic Equation using GRAPHING

ALGEBRA II TERMS Related to QUADRATIC Functions

ALGEBRA II TERMS Related to QUADRATIC Functions QUADRATIC FUNCTION A FUNCTION described by an EQUATION that can be written in the form: f(x) = ax 2 + bx + c where a  0

ALGEBRA II TERMS Related to QUADRATIC Functions f(x) = ax 2 + bx + c ax 2 is the QUADRATIC Term bx is the LINEAR Term c is the CONSTANT Term

ALGEBRA II The GRAPH of a QUADRATIC Function is a PARABOLA

ALGEBRA IIALGEBRA II The GRAPH of a QUADRATIC Function is a PARABOLA f(x) = x² +6x - 4

ALGEALGEBRA II f(x) = x² +6x - 4 AXIS of SYMMETRY x = - 3 The AXIS of SYMMETRY splits the PARABOLA evenly NAME the AXIS of SYMMETRY by the Equation of the Line

ALGEBRA II f(x) = x² +6x - 4 AXIS of SYMMETRY x = - 3 The AXIS of SYMMETRY splits the PARABOLA evenly NAME the AXIS of SYMMETRY by the Equation of the Line

ALGEBRA II f(x) = x² +6x - 4 AXIS of SYMMETRY x = - 3 VERTEX (- 3, -13) The VERTEX is the INTERSECTION of the AXIS of SYMMETRY and the PARABOLA. NAME the VERTEX by its (x, y) Coordinates.

ALGEBRA II QUADRATIC FUNCTION A FUNCTION described by an EQUATION that can be written in the form: f(x) = ax 2 + bx + c

ALGEBRA II QUADRATIC FUNCTION A FUNCTION described by an EQUATION that can be written in the form: f(x) = ax 2 + bx + c QUADRATIC EQUATION A Quadratic Function SET TO ZERO. 0 = ax 2 + bx + c

QUADRATIC EQUATION A Quadratic Function SET TO ZERO. 0 = ax 2 + bx + c The ROOTS or SOLUTIONS of a Quadratic Equation are the VALUES that make the EQUATION True.

ALGEBRA II QUADRATIC EQUATION A Quadratic Function SET TO ZERO. 0 = ax 2 + bx + c The ROOTS or SOLUTIONS of a Quadratic Equation are the VALUES that make the EQUATION True. Chapter 6 is all about the DIFFERENT METHODS of FINDING THE ROOTS

ALGEBRA II x 2 – 3x – 10 (1.5, ) x = 1.5 ( -2, 0) ( 5, 0)

How to GRAPH a QUADRATIC FUNCTION: 1.Get the Quadratic Function in EQUATION form. 2.Find the VERTEX X Coordinate 3.Make a table of 5 X points, with the 3 rd Point being the VERTEX. 4.Find the Y Coordinate for each X Point 5.CONNECT the Points.

x 2 + 5x + 6 How to GRAPH a QUADRATIC FUNCTION: 1.Get the Quadratic Function in EQUATION form. 2.Find the VERTEX X Coordinate 3.Make a table of 5 X points, with the 3 rd Point being the VERTEX. 4.Find the Y Coordinate for each X Point 5.CONNECT the Points.

How to GRAPH a QUADRATIC FUNCTION: 1.Get the Quadratic Function in EQUATION form. 2.Find the VERTEX X Coordinate 3.Make a table of 5 X points, with the 3 rd Point being the VERTEX. 4.Find the Y Coordinate for each X Point 5.CONNECT the Points. x 2 – 8x + 12

How to GRAPH a QUADRATIC FUNCTION: 1.Get the Quadratic Function in EQUATION form. 2.Find the VERTEX X Coordinate 3.Make a table of 5 X points, with the 3 rd Point being the VERTEX. 4.Find the Y Coordinate for each X Point 5.CONNECT the Points. (x + 2) 2 – 9

How to GRAPH a QUADRATIC FUNCTION: 1.Get the Quadratic Function in EQUATION form. 2.Find the VERTEX X Coordinate 3.Make a table of 5 X points, with the 3 rd Point being the VERTEX. 4.Find the Y Coordinate for each X Point 5.CONNECT the Points. x 2 – 4x + 4

How to GRAPH a QUADRATIC FUNCTION: 1.Get the Quadratic Function in EQUATION form. 2.Find the VERTEX X Coordinate 3.Make a table of 5 X points, with the 3 rd Point being the VERTEX. 4.Find the Y Coordinate for each X Point 5.CONNECT the Points. x 2 – 3x + 6

How to GRAPH a QUADRATIC FUNCTION: 1.Get the Quadratic Function in EQUATION form. 2.Find the VERTEX X Coordinate 3.Make a table of 5 X points, with the 3 rd Point being the VERTEX. 4.Find the Y Coordinate for each X Point 5.CONNECT the Points. x 2 – 9

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM m 2 + 3m = 4

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM 4v 2 – 8v – 5 = t

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM Y =- 4x 2 – 8x – 9

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM Y = 4x

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM Y =2x 2 – 6x – 4

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM Y =-2x 2 – x – 15

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM Y =x x + 225

Using a GRAPHING CALCULATOR to GRAPH Quadratic Functions 1.Get the function in y = form. Enter it in y = 2.Look at the GRAPH 3.Use 2 nd Calc, Value to complete the X, Y table 4.If needed, use 2 nd Calc to find ROOTS 5.If needed, use 2 nd Calc to find the VERTEX by finding the MINIMUM or MAXIMUM