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2.3Solving Quadratic Equations by Graphing and Factoring.notebook 1 December 11, 2013 Oct 810:07 AM 2.3Solving Quadratic Equations by Graphing and Factoring Warm Up Find the xintercept of each function. 1. f(x)=3x+9 2. f(x)=6x+4 Factor each expression. 3. 3x 2 12x 4. x 2 9x+18 5. x 2 49 Oct 911:35 AM Oct 98:26 AM Oct 103:30 PM MAKE SURE YOU HAVE YOUR TEXTBOOK TODAY!!!! Oct 810:10 AM Zero of a Function a value of the input x that makes the output f(x) equal zero *The zeros of a function are the xintercepts Zeros of a Function Oct 810:19 AM Finding Zeros by Using a Graph or Table Find the zeros of f(x)=x 2 +2x3 by using a graph and a table Step 1: Graph the function. Opens Upward/Downward: Axis of Symmetry: yintercept: vertex: Step 2: Use Symmetry and a table of values to find additional points.

2.3-Solving Quadratic Equations by Graphing and …...2.3 Solving Quadratic Equations by Graphing and Factoring.notebook 2 December 11, 2013 Oct 8 10:23 AM You try! Find the zeros

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Page 1: 2.3-Solving Quadratic Equations by Graphing and …...2.3 Solving Quadratic Equations by Graphing and Factoring.notebook 2 December 11, 2013 Oct 8 10:23 AM You try! Find the zeros

2.3­Solving Quadratic Equations by Graphing and Factoring.notebook

1

December 11, 2013

Oct 8­10:07 AM

2.3­Solving Quadratic Equations by Graphing and Factoring

Warm Up

Find the x­intercept of each function.

1. f(x)=­3x+9

2. f(x)=6x+4

Factor each expression.

3. 3x2­12x

4. x2­9x+18

5. x2­49

Oct 9­11:35 AM

Oct 9­8:26 AM Oct 10­3:30 PM

MAKE SURE YOU HAVE YOUR TEXTBOOK TODAY!!!!

Oct 8­10:10 AM

Zero of a Function­a value of the input x that makes the output f(x) equal zero

*The zeros of a function are the x­intercepts

Zeros of a Function

Oct 8­10:19 AM

Finding Zeros by Using a Graph or TableFind the zeros of f(x)=x2+2x­3 by using a graph and a table 

Step 1: Graph the function.

Opens Upward/Downward:

Axis of Symmetry:

y­intercept:

vertex:

Step 2: Use Symmetry and a table of values to find additional points.

Page 2: 2.3-Solving Quadratic Equations by Graphing and …...2.3 Solving Quadratic Equations by Graphing and Factoring.notebook 2 December 11, 2013 Oct 8 10:23 AM You try! Find the zeros

2.3­Solving Quadratic Equations by Graphing and Factoring.notebook

2

December 11, 2013

Oct 8­10:23 AM

You try!

Find the zeros of g(x)=­x2­2x+3 by using a graph and a table.

Oct 8­10:24 AM

Another way to find zeros of the function is using Algebra!

To find the zeros of f(x)=x2+2x­3, set the function equal to zero.

Oct 8­10:25 AM

The solutions to a quadratic equation of the form ax2+bx+c=0 are roots.

Roots

The roots of an equation are the values of the variable that make the equation true.

Oct 8­10:27 AM

You can find the roots of some quadratic equations by factoring and applying the Zero Product Property.

Oct 8­10:28 AM

Finding Zeros by Factoring 

Find the zeros of each function by factoring

A. f(x)=x2­8x+12

Oct 8­10:29 AM

B. g(x)=3x2+12x

Page 3: 2.3-Solving Quadratic Equations by Graphing and …...2.3 Solving Quadratic Equations by Graphing and Factoring.notebook 2 December 11, 2013 Oct 8 10:23 AM You try! Find the zeros

2.3­Solving Quadratic Equations by Graphing and Factoring.notebook

3

December 11, 2013

Oct 8­10:30 AM

You try!

1. f(x)=x2­5x­6

2. g(x)=x2­8x

Oct 8­10:31 AM

Practice

Page 82 #'s 1­17

Oct 8­10:31 AM