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Solving Quadratic Equations. Review of Solving Quadratic Equations. ax 2 +bx +c = 0 A quadratic equation is a 2nd degree equation whose graph is a parabola. Solve with Perfect Square Binomial. Get Perfect Squares on Both Sides of Equation. Take Square Root of Perfect Squares

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review of solving quadratic equations
Review of Solving Quadratic Equations

ax2 +bx +c = 0

A quadratic equation is a 2nd degree equation whose graph is a parabola.

slide3

Solve with Perfect Square Binomial

Get Perfect Squares on Both Sides of Equation.

Take Square Root of Perfect Squares

Solve Positive Number & Neg. Number

Check Answers by Putting into Original Eq.

slide4

Solve with Perfect Square Binomial

Get Perfect Squares Binomial.

Take Square Root of Both Sides of Eq

Simplify

Check Answers by Putting into Original Eq.

slide5

Solve Quadratic Eq. By Factoring

Set Eq = 0

Factor

Set Each Factor = 0

Check Answers by Putting into Original Eq.

what if you can t factor the equation
What If You Can’t Factor The Equation?

The “X” factor procedure

doesn’t work which means it

can not be factored

-36

4

review of a trinomial square
Review of a Trinomial Square

(x+5)2 = x2 + 10x + 25

When you square a binomial you get a TRINOMIAL SQUARE

what is completing the square
What is Completing The Square?

?

x2 + 10x +

WHAT WILL MAKE A TRINOMIAL SQUARE?

slide11

?

x2 + 10x +

b

It takes 25 ones to complete this square

Note that 25 is half of b squared

(10/2)2 = 52 = 25

slide12

2

b

2

Remember this to Complete The Square

add to complete the square
Add to Complete the Square

b

This is now a trinomial square

x 2 6x 9 is a trinomial square
x2+6x+9 is a Trinomial Square

x+3

x+3

x2+6x+9

(x+3)2 =x2 +6x+9

more examples of
More Examples of

CTS

Half of b Squared

Half of b Squared

more examples of1
More Examples of

CTS

Half of b Squared

more examples of2
More Examples of

CTS

Half of b Squared

solve by completing the square1
Solve by Completing The Square

First Put c on One Side of equation.

solve by completing the square2
Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Skip this step when a=1

solve by completing the square3
Solve by Completing The Square

b

First Put c on One Side of equation.

Divide by a

Complete The Square

ADD HALF OF b SQUARED

(b/2)2=(4/2)2=4

solve by completing the square4
Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

Write Trinomial Square as a Binomial Square

solve by completing the square5
Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

Write Trinomial Square as a Binomial Square

Square Root both sides

solve by completing the square6
Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

Write Trinomial Square as a Binomial Square

Square Root both sides

Solve for x (Note 2 Answers)

slide32

Solve by Completing The Square

First Put c on One Side of equation.

Divide equation by a

Complete The Square

(b/2)2=

4. Write Trinomial Square as a Binomial Square

5. Square Root both sides

6. Solve for x (Note 2 Answers)

slide33

Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

(b/2)2=(8/2)2=42=16

4. Write Trinomial Square as a Binomial Square

5. Square Root both sides

6. Solve for x (Note 2 Answers)

slide34

Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

(b/2)2=

4. Write Trinomial Square as a Binomial Square

5. Square Root both sides

6. Solve for x (Note 2 Answers)

slide35

Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

(b/2)2=(2/2)2=1

4. Write Trinomial Square as a Binomial Square

5. Square Root both sides

6. Solve for x (Note 2 Answers)

slide37

Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

(b/2)2=(6/2)2=32=9

4. Write Trinomial Square as a Binomial Square

5. Square Root both sides

6. Solve for x (Note 2 Answers)

slide38

Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

(b/2)2=(9/2)2= 81/4

4. Write Trinomial Square as a Binomial Square

5. Square Root both sides

6. Solve for x (Note 2 Answers)

slide39

Solve by Completing The Square

First Put c on One Side of equation.

Divide by a

Complete The Square

(b/2)2=(2/2)2=1

4. Write Trinomial Square as a Binomial Square

5. Square Root both sides

6. Solve for x (Note 2 Answers)

solve quadratic equations with the quadratic formula
Solve Quadratic Equations With The Quadratic Formula

So far we have solved quadratic equations with

FACTORING (Solves Equations with Integer Solutions) & COMPLETING THE SQUARE (Solves All quadratic equations)

THE QUADRATIC FORMULA ALSO SOLVES ALL QUADRATIC EQUATIONS

slide42

2

+

- b

X=

2 a

solve with quadratic equation1
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

solve with quadratic equation2
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

solve with quadratic equation3
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

Simplify Radical

solve with quadratic equation4
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

Simplify Radical

Solve for x

solve with quadratic equation6
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

solve with quadratic equation7
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

solve with quadratic equation8
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

Simplify Radical

solve with quadratic equation9
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

Simplify Radical

Solve for x

solve with quadratic equation10
Solve with Quadratic Equation

a=1

b

c

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

Simplify Radical

Solve for x

solve with quadratic equation11
Solve with Quadratic Equation

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

Simplify Radical

Solve for x

a=1

b

c

solve with quadratic equation12
Solve with Quadratic Equation

Put Equation into Std. Form (ax2+bx+c=0)

Plug a, b & c into the Quad. Eq.

Simplify Radical

Solve for x

a

b

c

the discriminant the discriminant equals b 2 4ac
The DiscriminantThe Discriminant equals b2-4ac

The Discriminant is what’s

under the RADICAL

the discriminant the discriminant equals b 2 4ac1
The DiscriminantThe Discriminant equals b2-4ac

2 Solutions if positive

1 Solution if 0

0 Solutions if negative

the discriminant tells you how many solutions or roots
The Discriminant tells you how many solutions or roots

y

x

This quadratic has two roots so the

Discriminant must be positive

the discriminant tells you how many solutions or roots1
The Discriminant tells you how many solutions or roots

X

This quadratic has one roots so the

Discriminant must be zero

the discriminant tells you how many solutions or roots2
The Discriminant tells you how many solutions or roots

X

This quadratic has no roots so the

Discriminant must be negative

find the number of solutions roots
Find The Number of Solutions (Roots)

Identify a, b & c.

Put values into the discriminant b2-4ac

If Pos. 2 Solutions If Zero 1 Solution If Neg. 0 Solutions

The discriminant is neg. so there are no solutions

determine the number of solutions or roots1
Determine The Number of Solutions or Roots

0 Solutions

2 Solutions

1 Solutions

singing the quadratic equation to the melody of pop goes the weasel
Singing the Quadratic Equation(To the melody of Pop Goes The Weasel)

Minus B plus or minus the square root

B squared minus 4AC

All over 2A, That’s the quadratic equation.

It’s the greatest equation of all time.

It even has a wonderful rhyme.

If you don’t know it, It would be a crime

That’s the quadratic equation.

Math is the most taught subject in the world

So you’d better believe me

Bone up to pass the SAT

You won’t end up a weasel.

slide66

SOLVING

QUADRATIC

EQUATIONS

Solutions are Roots

Where Graph crosses

the x-axis

what method to use
What Method To Use

• SquareRoot when there is a perfect square on one side of eq.

• Use “X” Factor when trinomial is factorable

• Use quadratic formula or complete the square if not factorable