Quadratics 5 Discriminant, Problem Solving, Intersecting Graphs.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Solve a quadratic equation having two solutions Solve x 2 – 2x = 3 by graphing. STEP 1 Write the equation in standard form. Write original equation.

Advertisements

4.8 Quadratic Formula and Discriminant

Solve Using Best Method

13-1 Introduction to Quadratic Equations  CA Standards 14.0 and 21.0  Quadratic Equations in Standard Form.

N 58 Graphical Solutions to Quadratic Functions Subject Content Reference: N6.7h GCSE Maths Number & Algebra.

Solving Systems Graphically Page 1. In 5-13, solve each quadratic-linear system graphically, showing the graphs of both equations on the same axes for.

Lesson 9.7 Solve Systems with Quadratic Equations

CHAPTER 7-1 SOLVING SYSTEM OF EQUATIONS. WARM UP  Graph the following linear functions:  Y = 2x + 2  Y = 1/2x – 3  Y = -x - 1.

Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations Topic 3: Solving Proportions involving linear and quadratic functions. Topic.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

Substitute 0 for y. Write original equation. To find the x- intercept, substitute 0 for y and solve for x. SOLUTION Find the x- intercept and the y- intercept.

CA STANDARDS 20.0: Students use the quadratic formula to find the roots of a second-degree polynomial and to solve quadratic equations. Agenda 1.) Lesson.

Using square roots to solve quadratic equations. 2x² = 8 22 x² = 4 The opposite of squaring a number is taking its square root √ 4= ± 2.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

1) What does x have to be for 3x = 0? 1) What does x have to be for 3(x -2) = 0 2) What does x have to be for (x–2) (x+3) = 0.

3.1 Solving equations by Graphing System of equations Consistent vs. Inconsistent Independent vs. Dependent.

3.6 Solving Absolute Value Equations and Inequalities

Chapter 2: Equations and Inequalities

Section 4.7 – The Quadratic Formula Students will be able to: To solve equations using the Quadratic Formula To determine the number of solutions by using.

3.7 Absolute value DAY 2. Solve for x----no notes on this slide (just watch). |x| = 5 |x + 2| = 5 x = 5 or x = -5 x + 2 = 5 or x + 2 = -5 x =

More about Quadratic Equations November 16, 2009.

Quadratics Solving Quadratic Equations. Solving by Factorising.

Chapter 6 Test Prep 6-3 through 6-5: Solving Quadratic Equations 6-6: Graphing Quadratic Functions Application Problems Choose a section to work on. At.

Warmup  1.) 4x 2 = 202.) 3x = 29  3.)4.)  5.)6.)

Solving a Trigonometric Equation Find the general solution of the equation.

Topics: Topic 1: Solving Linear Equations Topic 2: Solving Quadratic Equations Topic 3: Solving Proportions involving linear and quadratic functions. Topic.

Notes Over 5.6 Quadratic Formula

ANSWERS!. Completing the Square Level 1 Answers Completing the Square Level 2 Answers.

EXAMPLE 1 Solve a system graphically Graph the linear system and estimate the solution. Then check the solution algebraically. 4x + y = 8 2x – 3y = 18.

QUADRATIC FUNCTIONS AND EQUATIONS Ch. 4.7 The Quadratic Formula EQ: HOW CAN YOU SOLVE QUADRATIC EQUATIONS BY USING THE QUADRATIC FORMULA? I WILL SOLVE.

2( ) 8x + 14y = 4 -12x – 14y = x = x = 4 8x + 14y = 4 8(4) + 14y = y = y = -28 ___ ___ y = -2 The solution is (4, -2)

Warm up ON A SEPARATE SHEET OF PAPER, ANSWER THE FOLLOWING:

To find the solution of simultaneous equations graphically: 1)

3.3 – Solving Systems of Inequalities by Graphing

Solving Nonlinear Systems

Solving Quadratic Equations by the Complete the Square Method

Solving Quadratic Equations by Graphing

Solve x2 + 2x + 24 = 0 by completing the square.

Solve Quadratic Systems

Solve a system of linear equation in two variables

4.8 The Quadratic Formula and the Discriminant

Unit 7 Day 4 the Quadratic Formula.

Class Notes 11.2 The Quadratic Formula.

Points of intersection of linear graphs an quadratic graphs

Quadratics 7. Quadratic Graphs.

Quadratic Functions and Equations

Solving Systems of Linear and Quadratic Equations

USING GRAPHS TO SOLVE EQUATIONS

Systems of Linear and Quadratic Equations

Click the problem to show the answers.

Quadratic Equations.

Unit 7, Lesson 1 Trigonometry / Pre-Calculus

Solving Systems of Linear and Quadratic Equations

Bellwork 1/24 Solve #1 and then do #2 1.) x + y = 5 2.) 3x + 2y = 12

Algebra 1 Mini Posters Systems of Linear and Quadratic Equations

Solving Simultaneous equations by the Graphical Method

Objectives Identify solutions of linear equations in two variables.

Quadratic Systems. What you’ll learn

Graphing Systems of Equations

Warm-Up 1) Sketch a graph of two lines that will never intersect.

Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER

3.5 Solving Nonlinear Systems

Using the Quadratic Formula to Solve Quadratic Equations

Where do these graphs intersect

Using the Discriminant and writing quadratic equations

1.) What is the value of the discriminant?

6-1 System of Equations (Graphing)

Wang991.wordpress.com Relation and function Click when ready 

Intersection Method of Solution

Use Graphs of Functions

Presentation transcript:

Quadratics 5 Discriminant, Problem Solving, Intersecting Graphs

The Discriminant (∆)

Example 1 (Ex1E6)

Example 2

Problems Page 35 Exercise 1E6 Questions 1, 2, 3

Problem Solving with Quadratics Read question carefully. Draw a diagram if appropriate to the question. Use the information to write an equation. Solve the equation Examine the solutions to see if they are appropriate to the problem. Give your answer in a sentance.

Example 3

Example 4

Example 5

Problems Page 36 Exercise 1F Questions 1, 2, 3, 4, 5, 6, 8, 9.

Intersecting Graphs

Example 6

Problems Page 40 Exercise 1G Questions 1, 2(a) (c) (e) (g).