Chapter 9 review
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Chapter 9 Review. Square Roots and Radicals. Try some: Simplify these:. More examples:. How would you solve the equation: x 2 = 4 (take the square root of each side!). * Remember, the square root of a positive # has 2 answers! (one + and one -). Solving Quadratic Equations.

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Chapter 9 Review

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Chapter 9 review

Chapter 9 Review

Square Roots and Radicals


Chapter 9 review

  • Try some:

  • Simplify these:


Chapter 9 review

  • More examples:


How would you solve the equation x 2 4 take the square root of each side

How would you solve the equation:x2 = 4(take the square root of each side!)

* Remember, the square root of a positive # has 2 answers! (one + and one -)


Solving quadratic equations

Solving Quadratic Equations

  • Solve. 3(x-2)2=21

  • Solve. 3 - 5x2 = -9

    -3 -3

    -5x2 = -12

    -5 -5

    x2 =

3 3

(x-2)2 = 7


More examples

More Examples!

4. Solve.

  • Solve. 4x2-6=42

    +6 +6

    4x2=48

    4 4

    x2 = 12


Rationalizing the denominator

Rationalizing the Denominator

You CANNOT leave a radical in the denominator of a fraction!

No tents in the basement!!!!

(the numerator is OK)

Just multiply the top & bottom of the fraction by the radical to “rationalize” the denominator.


Properties of square roots

Properties of Square Roots

(a>0 and b>0)

  • Product Property –

  • Quotient Property-

Example:

Example:


Chapter 9 review

Simplify each expression.

A.

Find a perfect square factor of 32.

Product Property of Square Roots

B.

Quotient Property of Square Roots


Chapter 9 review

Simplify each expression.

C.

Product Property of Square Roots

D.

Quotient Property of Square Roots


Chapter 9 review

Simplify each expression.

E.

Find a perfect square factor of 48.

Product Property of Square Roots

F.

Quotient Property of Square Roots

Simplify.


Chapter 9 review

Simplify each expression.

G.

Product Property of Square Roots

H.

Quotient Property of Square Roots


Examples

Examples

1.

2.

3.


More examples1

More Examples!

1.

2.

Can’t have a tent in the basement!


Chapter 9 review

Simplify by rationalizing the denominator.

Multiply by a form of 1.

= 2


Chapter 9 review

Simplify the expression.

Multiply by a form of 1.


Chapter 9 review

Simplify by rationalizing the denominator.

Multiply by a form of 1.


Chapter 9 review

Simplify by rationalizing the denominator.

Multiply by a form of 1.


Chapter 9 review

1. Estimate to the nearest tenth.

6.7

Simplify each expression.

2.

3.

4.

5.


Solving quadratic equations using the quadratic formula

General equation of a quadratic:

Solving Quadratic Equations using the Quadratic Formula

You must get equation equal to zero before you determine a, b, and c.

Quadratic Formula:

Notice where the letters come from for the formula

We use the quadratic formula when something can not be factored. However, it also works for factorable quadratic equations as well.


Chapter 9 review

Solve.

Ex. 1


Chapter 9 review

Solve.

Ex. 2


Chapter 9 review

Solve.

Ex. 3


Chapter 9 review

Solve.

Ex. 4


Chapter 9 review

Suppose a football player kicks a ball and gives it an initial upward velocity of 47ft/s. The starting height of the football is 3ft. If no one catches the football, how long will it be in the air?

Ex. 5

NOTE: For your homework tomorrow night, DO NOT answer the question. I want you to draw a sketch of what you think this picture would look like on a graph. Tell me what the x-axis symbolizes, what the y-axis symbolizes, and what the zeros represent in the problem.

What does the x-axis stand for?

What does the y-axis stand for?

What do the zeros represent?

Time the ball is in the air

Height of the ball

The amount of time it takes the ball to hit the ground.


Chapter 9 review

Before you can find a,b, and c, you must get equation = to 0.

Type what is under the radical exactly as written on your calculator.

Simplify the radical

Divide by the denominator, if you can

Roots:


Chapter 9 review

Simplify the radical

Divide by the denominator, if you can. Since I can’t, divide by GCF

Roots:

Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form.


Chapter 9 review

Since we are solving to the nearest tenth, we do not need to simplify the radical!

Be careful when typing this into your calculator. I recommend that you type in the numerator then hit enter, then divide by denominator!

Roots:

Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth.


Chapter 9 review

Roots:

Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth.


Chapter 9 review

Roots

Solve the quadratic equation by using the quadratic formula and round answers to the nearest tenth.


Chapter 9 review

Divide by the denominator, if you can. Since I can’t, divide by GCF

Roots:

Solve the quadratic equation by using the quadratic formula and leave answers in simplest radical form.


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