5.2 Solving Quadratic Equations by Factoring

Slides:

Advertisements

Similar presentations

I can use the zero product property to solve quadratics by factoring

Advertisements

Calculator Shortcut – Solving Trinomials

Day 5 Simplify each expression: Solving Quadratic Equations I can solve quadratic equations by graphing. I can solve quadratic equations by using.

Solving Quadratic (and polynomial) Equations by Factoring.

5.1 Graphing Quadratic Functions Do now: Make up three examples of linear functions. How do you know they are linear? OBJ: to graph quadratic functions.

Section 1.2 Linear Equations and Rational Equations

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.

5.2: Solving Quadratic Equations by Factoring (p. 256)

1.3 Solving Quadratic Equations by Factoring (p. 18) How can factoring be used to solve quadratic equation when a=1?

Notes - Solving Quadratic Equations in Factored Form If ab = 0, then a = 0 or b = 0 If the product of two factors is zero, then at least one of the factors.

Solving Quadratic Equations

Section 1.5 Quadratic Equations. Solving Quadratic Equations by Factoring.

Solving Quadratic Equations by Graphing 4 Lesson 10.2.

Solving Quadratic Equations by Graphing. Essential Question Where are the solutions to quadratic equations located on the graph of the parabola?

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

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

Aim: How Do We Solve Quadratic Equations by Factoring

Solving Quadratic (and polynomial) Equations by Factoring.

SOLVING QUADRATICS DAY 3 (IN THE CALCULATOR) EQ: How can points of intersection be used to solve any equation?

Factoring by Grouping ALGEBRA 1 LESSON 9-8 (For help, go to Lessons 9-2 and 9-3.) Find the GCF of the terms of each polynomial. 1.6y y – 42.9r 3.

Solving Quadratic Equations by Factoring. To solve a quadratic eqnuation by factoring, you must remember your factoring patterns!

§ 6.6 Solving Quadratic Equations by Factoring. Martin-Gay, Beginning and Intermediate Algebra, 4ed 22 Zero Factor Theorem Quadratic Equations Can be.

Solving Quadratic Equations Using the Zero Product Property March 18, 2014.

4.4: Factoring (Quadratic Equations) Algebra II. Ex. 1 15x² - 2x - 8.

Solving Quadratics Review. We must solve to get x 2 by itself 1 st !

Solving Systems of Linear and Quadratic Equations.

Objective: Use factoring to solve quadratic equations. Standard(s) being met: 2.8 Algebra and Functions.

The Real Roots of Polynomials

Solving Polynomial Equations

6.3 notes Solving Quadratics.

Solve equations by factoring.

5.2: Solving Quadratic Equations by Factoring

Objectives Solve quadratic equations by factoring.

UNIT 1 TEST REVIEW ALGEBRA II

Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

1.4 Solving Quadratic Equations by Factoring

Solving Quadratic Equations

Systems of Equations Lesson 41: Solve by using a matrix

Warm Up Factor completely. 1. 2y3 + 4y2 – 30y 2y(y – 3)(y + 5)

A quadratic equation is written in the Standard Form,

Solving Quadratic Equations by Graphing

SECTION 9-3 : SOLVING QUADRATIC EQUATIONS

Solving Quadratic Equation by Graphing

Section 1.2 Linear Equations and Rational Equations

Solving Quadratic Equations by Factoring March 16, 2015

Solving Quadratics by Factoring

Notes - Solving Quadratic Equations in Factored Form

Objectives Solve quadratic equations by graphing or factoring.

WELCOME BACK WARM UP! Find The roots of the given quadratic: x2+7x+6=0 A.) {0,6} B.) {-6,0} C.) {-6,-1} D.) {1,6}

Finding Solutions by graphing

4.3 Solving Quadratic Equations by Factoring

Objectives Solve quadratic equations by graphing or factoring.

Warm Up Find the x-intercept of each function. 1. f(x) = –3x + 9 3

Chapter 5.1 & 5.2 Quadratic Functions.

10.4 Solving Quadratic Equations in Factored Form

Using Factoring To Solve

Section 9.5 Day 1 Solving Quadratic Equations by using the Quadratic Formula Algebra 1.

You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.

Solving Quadratic Equations by Factoring

Solving Quadratic Equations by Factoring

Solving Polynomial Equations in Factored Form

Solving Quadratic Equations by Factoring

Warm up Factor Completely 5x2 – 13x + 6 x2 – 9y2 3) y2 + 2y – 48

9-5 Factoring to Solve Quadratic Equations

Warm-Up 2.10 Solve the following. 8x2 + 18x + 9 = 0

Objective SWBAT solve polynomial equations in factored form.

Solving Equations by Factoring

Solving Quadratic Equations by Factoring March 11, 2016

4.3: Solving (Quadratic Equations) by Factoring

Presentation transcript:

5.2 Solving Quadratic Equations by Factoring OBJ: To factor quadratic expressions, solve quadratic equations by factoring, and find zeros of quadratic functions 5.2 Solving Quadratic Equations by Factoring *To solve a quadratic eqn. by factoring, you must remember HOW TO FACTOR! Do Now: How to Factor handout

Zero Product Property Let A and B be real numbers or algebraic expressions. If A(B) = 0, then A = 0 or B = 0. *This means that If the product of 2 factors is zero, then at least one of the 2 factors had to be zero!

Ex 1: Solve x2 + 3x - 18 = 0 x2+3x-18=0 Factor the left side (x+6)(x-3)=0 set each factor =0 x+6=0 OR x-3=0 solve each eqn. -6 -6 +3 +3 x=-6 OR x=3 check your solutions!

Ex 2: Solve 2t2 - 17t + 45 = 3t - 5 2t2-17t+45=3t-5 Set eqn. =0 2t2-20t+50=0 factor out GCF of 2 2(t2-10t+25)=0 divide by 2 t2-10t+25=0 factor left side (t-5)2=0 set factors =0 t-5=0 solve for t +5 +5 t=5 check your solution!

Ex 3: Solve 3x – 6 = x2 – 10 3x-6=x2-10 Set = 0 0=x2-3x-4 Factor the right side 0=(x-4)(x+1) Set each factor =0 x-4=0 OR x+1=0 Solve each eqn. +4 +4 -1 -1 x=4 OR x=-1 Check your solutions!

Finding the Zeros of an Equation *The Zeros of an equation are the x-intercepts ! First, change y to a zero. Now, solve for x. The solutions will be the zeros of the equation. lets try graphing on the calculator: 2nd CALC option “2:zeros” left bound? enter right bound? enter guess? enter

Ex 4: Find the Zeros of y = x2 – x – 6 y=x2-x-6 Change y to 0 0=x2-x-6 Factor the right side 0=(x-3)(x+2) Set factors =0 x-3=0 OR x+2=0 Solve each equation +3 +3 -2 -2 x=3 OR x=-2 Check your solutions! - If you were to graph the eqn., the graph would cross the x-axis at (-2,0) and (3,0).