4.5 Quadratic Equations Wherever the graph of a function f(x) intersects the x-axis, f(x) = 0. A value of x for which f(x) = 0 is a zero of the function.

Slides:

Advertisements

Similar presentations

7-5 solving quadratic equations

Advertisements

I.Vocabulary A.Factoring is rewriting an expression as a product of its factors. B.Greatest Common Factor (GCF) of an expression is a common factor of.

Quadratic Functions By: Cristina V. & Jasmine V..

Using the Zero-Product Property to Solve a Quadratic

WARM UP What do you remember?.... QUADRATIC EQUATIONS SECTION 5.5.

2-3 solving quadratic equations by graphing and factoring

Solve an equation with an extraneous solution

Quadratic Equations, Functions, and Models

6.5 – Solving Equations with Quadratic Techniques.

5.3.2 – Quadratic Equations, Finding Zeroes. Recall, we went over how to factor quadratics that are trinomials Example. Factor the expression x 2 + 7x.

Solve an equation with an extraneous solution

Section 4.5 – Quadratic Equations

Quadratics Solving equations Using “Completing the Square”

Essential Question: How do you use the quadratic formula and the discriminant? Students will write a summary including the steps for using the quadratic.

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.

Section 5.3 Factoring Quadratic Expressions

Solving Quadratic Equations by Graphing!. Quadratic functions vs. Quadratic equations Quadratic fxns are written in the following form f(x) = ax² + bx.

Copyright © 2011 Pearson, Inc. P.5 Solving Equations Graphically, Numerically and Algebraically.

Factoring to Solve Quadratic Equations

What you will learn How to solve a quadratic equation using the quadratic formula How to classify the solutions of a quadratic equation based on the.

QUADRATIC EQUATIONS §5.5. OBJECTIVES By the end of today, you should be able to… Solve quadratic equations by factoring and graphing. What does it mean.

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

4-5 Quadratic Equations Solve quadratic equations by graphing and factoring.

Holt Algebra Solving Quadratic Equations by Graphing and Factoring A trinomial (an expression with 3 terms) in standard form (ax 2 +bx + c) can be.

Today’s entrance ticket… Factor! Be sure to ask any questions before the quiz!! You should have studied last night and be prepared today!

MM2A3 Students will analyze quadratic functions in the forms f(x) = ax 2 +bx + c and f(x) = a(x – h) 2 = k. MM2A4b Find real and complex solutions of equations.

Example 1A Solve the equation. Check your answer. (x – 7)(x + 2) = 0

Section 5-4(e) Solving quadratic equations by factoring and graphing.

SOLVING QUADRATIC EQUATIONS Factoring Method. Warm Up Factor the following. 1. x 2 – 4x – x 2 + 2x – x 2 -28x + 48.

Warm Up Identify the Roots and the Zeros of this quadratic.

Solving Quadratic Equations by Factoring. The quadratic equation is written in the form ax 2 + bx + c = 0 To solve quadratic equations by factoring we.

Solving Quadratic Formula using the discriminant.

Solving Quadratic Equations. Factor: x² - 4x - 21 x² -21 a*c = -21 b = -4 x + = -21 = x 3x3x x 3 (GCF) x-7 (x – 7)(x + 3)

Solving Quadratic Equations by Factoring. Zero-Product Property If ab=0, then either a=0, b=0 or both=0 States that if the product of two factors is zero.

6-2 Solving Quadratic Equations by Graphing Objectives: Students will be able to 1)Solve quadratic equations by graphing 2)Estimate solutions of quadratic.

Warm Up 1.) What is the graph of the function y = -x 2 + 4x + 1?

SAT Problem of the Day. 5.3 Factoring Quadratic Expressions 5.3 Factoring Quadratic Expressions Objectives: Factor a quadratic expression Use factoring.

Lesson: Objectives: 5.1 Solving Quadratic Equations - Graphing  DESCRIBE the Elements of the GRAPH of a Quadratic Equation  DETERMINE a Standard Approach.

4.2 Standard Form of a Quadratic Function The standard form of a quadratic function is f(x) = ax² + bx + c, where a ≠ 0. For any quadratic function f(x)

Homework (Tuesday, 11/3) Lesson 2.03 packet page 4 and 5.

Warm-Up Solve each equation by factoring. 1) x x + 36 = 02) 2x 2 + 5x = 12.

9.4: FACTORING TO SOLVE QUADRATIC EQUATIONS. ZERO-PRODUCT PROPERTY WITH EXAMPLES: Zero-Product Property: If ab = 0, then a = 0 or b = 0. ( If the quadratic.

Quadratic Equations Chapter 4 Section 5, Section 7 and Section 8.

Solving Quadratic Functions by Factoring. Factoring Review.

A factored form of x 2 + 5x - 24 is — A (x − 4)(x + 6) B (x − 3)(x + 8) C (x − 2)(x + 12) D (x − 6)(x + 4) Which of the following equals when factored.

WARM UP What are the solutions of each equation? 1.) x = 4 2.) x = 0 3.) x 2 – 49 = 0.

Notes P.5 – Solving Equations. I. Graphically: Ex.- Solve graphically, using two different methods. Solution – See graphing Calculator Overhead.

Solving Equations Graphically, Numerically, and Algebraically

Solving Quadratic Equation by Graphing

Solving Equations by Factoring

Objectives Solve quadratic equations by factoring.

Tuesday You need: - Calculator - Whiteboard, marker, eraser.

Solving Quadratic Equation and Graphing

5.6 – The Quadratic Formula And Ch 5 Review

The Quadratic Formula.

Solving Quadratic Equations by Factoring

9-6 The Quadratic Formula and Discriminant

Warm-Up 5 minutes List all the factors of each number. 1) 10 2) 48

Solving Quadratic Equations by Factoring

Using Factoring To Solve

Objective Solve quadratic equations by graphing.

Objective Solve quadratic equations by factoring..

Standard Form Quadratic Equation

Warm-Up 5 minutes Factor the following expressions: 2) x2 - 3x

Chapter 6 Section 5.

Solve Quadratics by Graphing ax2 +bx + c

Homework Lesson 5.3_page 296 # ALL.

Solving Quadratic Equations by Graphing

Solving Equations by Factoring

Solving Quadratic Equations by Factoring

Presentation transcript:

4.5 Quadratic Equations Wherever the graph of a function f(x) intersects the x-axis, f(x) = 0. A value of x for which f(x) = 0 is a zero of the function. To find the zeros of a quadratic function y = ax 2 + bx + c, solve the related quadratic equation 0 = ax 2 + bx + c.

Zero-Product Property You can solve some quadratic equations in standard form by factoring the quadratic expression and using the Zero-Product Property. Zero-Product Property: If ab = 0, then a = 0 or b = 0.

Solving a Quadratic Equation by Factoring What are the solutions of the quadratic equation x 2 – 5x + 6 = 0? Factor the quadratic expression. (x – 2)(x – 3) = 0 Use the Zero-Product Property. x – 2 = 0 or x – 3 = 0 x = 2 or x = 3 The solutions are x = 2 and x = 3.

Solving a Quadratic Equation with Tables What are the solutions of the quadratic equation 5x x + 14 = 2 – 2x? 5x x + 14 = 2 – 2x 5x x + 12 = 0 Use your calculator’s table feature to find the zeros.

Solving a Quadratic Equation with Tables Notice that when x = -6, y = 0. So, x = -6 is one zero. The second zero is between x = -1 and x = 0 – notice the change in sign for y – values. Change the x-interval to.1. The second zero is x = The solutions are x = -6 and x = -0.4.

Solving a Quadratic Equation by Graphing What are the solutions of the quadratic equation 2x 2 + 7x = 15? 2x 2 + 7x = 15 2x 2 + 7x – 15 = 0 Use your calculator’s zero option in CALC feature to find the zeros. The solutions are x = -5 and x = 1.5.

More Practice!!!!! Homework – Textbook p. 229 #10 – 36 even.