WARM UP What do you remember?...

QUADRATIC EQUATIONSSECTION 5.5

OBJECTIVES

By the end of this part of the lesson, you should be able to…

• Simplify square roots.

• Solve quadratic equations by finding square roots.

SOLVING QUADRATIC EQUATIONSWITH SQUARE ROOTS

02 cax

If a quadratic equation is missing the b term we can solve using square roots.

The goal is to get x by itself .

EXAMPLE 1: SIMPLIFYING RADICALS

24.

49

81.

45.

c

b

a

EXAMPLE 2: SIMPLIFYING RADICALS

121

27.

10.

32.

c

b

a

EXAMPLE 4: SOLVING BY FINDING SQUARE ROOTS

5x 2 1800

Step 1) Rewrite in form ax2 = c.

Step 2) Isolate x2.

Step 3) Simplify.

Step 4) Take the square root of each side.

EXAMPLE 5: SOLVING BY FINDING SQUARE ROOTS

EXAMPLE 6: SOLVING BY FINDING SQUARE ROOTS

4x 2 250

EXAMPLE 6: SOLVING BY FINDING SQUARE ROOTS

OBJECTIVES

By the end of today, you should be able to…

• Solve quadratic equations by factoring and graphing.

What does it mean to solve an equation?

Quick Review:When you solve an equation, you’re finding the values that make the statement true.

QUADRATIC EQUATIONS

Remember - the standard form of a quadratic equation is ax2 + bx + c = 0, where a ≠ 0.

You can solve some quadratic equations in standard form by factoring the quadratic expression and then using…

The Zero-Product Property!

THE ZERO-PRODUCT PROPERTY

The Zero-Product Property helps us solve quadratic equations that have been factored.

The Zero-Product Property states:If ab = 0, then a = 0 or b = 0.

For example, if (x + 3)(x - 7)=0, then (x + 3) = 0 or (x - 7) = 0.

EXAMPLE 1: SOLVING BY FACTORING

Solve by factoring.Step 1) Write in standard form.

Step 2) Factor.

Step 3) Use the Zero-Product Property.

Step 4) Solve for x.

EXAMPLE 2: SOLVING BY FACTORING

Solve by factoring.Step 1) Write in standard form.

Step 2) Factor.

Step 3) Use the Zero-Product Property.

Step 4) Solve for x.

EXAMPLE 3: SOLVING BY FACTORING

Solve by factoring.Step 1) Write in standard form.

Step 2) Factor.

Step 3) Use the Zero-Product Property.

Step 4) Solve for x.

EXAMPLE 4: SOLVING BY FACTORING

Solve by factoring.Step 1) Write in standard form.

Step 2) Factor.

???

SOLVING BY GRAPHING

You can solve a quadratic equation in standard form by graphing its related quadratic function,

y = ax2 + bx +c and finding the x-intercepts.

Quadratic equation cannot

be solved by factoring

Quadratic equation can be solved by graphing!

SOLVING BY GRAPHING

1)Write in standard form2)Graph in your calculator3)Find the x-intercepts

SOLVING BY GRAPHING

Equation X-intercept(s)

x2 – 6x + 9

x2 + 4x – 5

HOMEWORK

Worksheet 5.5 #s 1, 3, 7, 11, 30, 34, 53, 60

Systems Projects – due Monday!