6.1 Solving Quadratic Equations by Graphing Need Graph Paper!!! Objective: To write functions in quadratic form To graph quadratic functions To solve quadratic equations by graphing

Vocabulary Quadratic function- Quadratic term- Linear term- Constant term- Parabola- the graph of a quadratic function Axis of Symmetry- a line that makes the parabola symmetric Vertex- the minimum or maximum point of the parabola Zeros- the x-intercepts of the parabola

Identify the quadratic term, the linear term, and the constant term. 1) 2) 3)

Use the related graph of each equation to determine its solutions and find the minimum or maximum point. 1) 2)

Graph each function. Name the vertex and axis of symmetry. 3)

Graph each function. Name the vertex and axis of symmetry. 4)

Solve by graphing. (Find the roots) 5)

Solve by graphing. (Find the roots) 5) (3x + 4)(2x + 7) = 0

Assignment 6.1 Page 339 (17-29 odd), (35- 41 odd), 49, 50, 51, 52

6.2 Solving Quadratic Equations by Factoring Objective: 1) To solve problems by factoring

Solve by using he zero product property. 1) 2) 3)

Solve by using he zero product property. 4) (3y – 5)(2y + 7) = 0 5) x(x – 1) = 0 6)

Solve by using he zero product property. 7) 8)

Assignment 6.2 Page 344 (11-33 odd), 41, 43, 44, 45, 46

Objective: 1) To solve quadratic equations by completing the square

Solve by completing the square. Steps The quadratic and linear term must be on one side of the equation and the constant must be on the other side. The quadratic term must have a coefficient of 1. Find c by taking half of the linear term and squaring it. 1)

Solve by completing the square. Steps The quadratic and linear term must be on one side of the equation and the constant must be on the other side. The quadratic term must have a coefficient of 1. Find c by taking half of the linear term and squaring it. 2)

Solve by completing the square. Steps The quadratic and linear term must be on one side of the equation and the constant must be on the other side. The quadratic term must have a coefficient of 1. Find c by taking half of the linear term and squaring it. 3)

Assignment 6.3 Page 351 (21-35 odd) 41, 43, 44, 46, 47

6.4 The Quadratic Formula and the Discriminant Objective: To solve quadratic equations by using the quadratic formula To use the discriminant to determine the nature of the roots of quadratic equations

Use quadratic formula to solve each equation. (1.)

Use quadratic formula to solve each equation. (2.)

Discriminant a Perfect Square? Examples Value of Discriminant a Perfect Square? Nature of Roots 1 Greater than zero Yes 2 real, rational #’s 2 2 real, Irrational #’s 3 Less than zero na 2 imaginary #’s 4 Zero 1 real #

Find the value of the discriminant for each quadratic equation Find the value of the discriminant for each quadratic equation. Then describe the nature of the roots. 3) 4)

Find the value of the discriminant for each quadratic equation Find the value of the discriminant for each quadratic equation. Then describe the nature of the roots. 5) 6)

Assignment 6.4 Page 357 (17-29 odd), 34, 35, 36, 37, 38

6.5 Sum and Product of Roots Objective: To find the sum and product of the roots of quadratic equations To find a quadratic equation to fit a given condition

Quadratic equations can have up to 2 real roots (answers). The sum and the product of these roots can be used to write a quadratic equation. Quadratic Equation Sum of Roots Product of Roots

(Denominators must be the same) Write a quadratic equation that has roots ¾ and –12/5. (Denominators must be the same) Sum of Roots Product of Roots

(Show the easier way to solve these problems) Write a quadratic equation that has roots 3/2 and 1/4. (Show the easier way to solve these problems)

(3) Write a quadratic equation that has roots 7 – 3i and 7 + 3i.

(4) Write a quadratic equation that has roots 6 and -9.

(5) Write a quadratic equation that has roots .

Assignment 6.5 Page 363 (17-26), For (29-37 odd) solve each equation by using factoring, completing the square, or quadratic formula. Use each method at least once. 47, 48, 49, 51, 52

6.6 Analyzing Graphs of Quadratic Functions Need Graph Paper!!! Objective: To graph quadratic functions of the form 2) To determine the equation of a parabola by using points on its graph.

Write the equation in the form Write the equation in the form . Then name the vertex, axis of symmetry, and the direction of the opening. 1) 2)

Write the equation in the form Write the equation in the form . Then name the vertex, axis of symmetry, and the direction of the opening. 3) 4)

Write the equation for each parabola and then state the domain and range in interval notation. 5) (1, 4) (3, 4) (2, 0)

Write the equation for each parabola and then state the domain and range in interval notation. 6) (-3, 6) (-5, 2) (-1, 2)

Write the equation for the parabola that passes through the given points. 7) (0, 0), (2, 6), (-1, 3) 8) (1, 0), (3, 38), (-2, 48)

Graph each function in the form Graph each function in the form . Then name the vertex, axis of symmetry, and the direction of the opening. Write the domain and range in interval notation. 9)

Graph each function in the form Graph each function in the form . Then name the vertex, axis of symmetry, and the direction of the opening. Write the domain and range in interval notation. 10)

Assignment 6.6 Page 373 (19-49 odd), 58, 62, 63, 64

6.7 Graphing and Solving Quadratic Inequalities Objective: To graph quadratic inequalities To solve quadratic inequalities in one variable.

Use the General Form to graph parabolas (Complete the Square) 1) Vertex: ( , ) Axis of Symmetry: x= Opening: Left Point and Right Point (x)

Use the General Form to graph parabolas (Complete the Square) 2) Vertex: ( , ) Axis of Symmetry: x= Opening: Left Point and Right Point (x)

Solve each inequality. (1) Solve of x (3) (2) Plot x’s on # line (3) Test point in each region (yes or no) (4) Write inequality (5) Write answer in interval notation

Solve each inequality. (1) Solve of x (4) (2) Plot x’s on # line (3) Test point in each region (yes or no) (4) Write inequality (5) Write answer in interval notation

Solve each inequality. (1) Solve of x (5) (x – 1)(x + 4) (x – 3) > 0 (2) Plot x’s on # line (3) Test point in each region (yes or no) (4) Write inequality (5) Write answer in interval notation

Assignment 6.7 Page 382 (27-53 odd), 63, 65, 66, 67, 68, 69, 70, 71

Unit 6 Review Exploring Quadratic Functions and Inequalities

Unit 6 Test is worth 100 points Covers sections 6.1 – 6.7 Study notes and hw Unit 6 Test Review Page 400 (11-53 odd) Page 357 (19, 23, 27) Page 382 (39, 47, 51) Page 352 (41)- worth 18 points on test

Sum and Product of Roots Items on the Test Quadratic function Quadratic term Linear term Constant term Parabola Axis of Symmetry Vertex Zeros Completing the Square Quadratic Formula Discriminant Sum and Product of Roots Domain Range Interval Notation Intercepts Quadratic Inequalities