1. 5-Minute Check on Chapter 2
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5-Minute Check on Chapter 2
Evaluate 42 - |x - 7| if x = -3
Find 4.1  (-0.5)
Simplify each expression
3. 8(-2c + 5) + 9c (36d – 18) / (-9)
A bag of lollipops has 10 red, 15 green, and 15 yellow lollipops. If one is chosen at random, what is the probability that it is not green?
Which of the following is a true statement
Standardized Test Practice: A
8/4 < 4/8 B
-4/8 < -8/4 C
-4/8 > -8/4 D
-4/8 > 4/8
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2. Solving Quadratic Equations by Completing the Square
Lesson 10-3
Solving Quadratic Equations by Completing the Square

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4. Transparency 3a

5. Objectives Solve quadratic equations by finding the square root
Solve quadratic equations by completing the square

6. Vocabulary
Completing the square –

7. Multiplication and Division PoE
Properties of Equality (PoE) are based on the concept that as long as you do the same thing to both sides of an equation, then you have not changed anything.
Multiplication PoE
For any numbers a, b, and c, if a = b, then ac = bc
You can multiply both sides of an equation by the same thing without changing the equation
Division PoE
For any numbers a, b, and c with c ≠ 0, if a = b, then a/c = b/c
You can divide both sides of an equation by the same thing without changing the equation
Multiplication and division are reciprocal actions

8. Example 1
Solve by taking the square root of each side. Round to the nearest tenth if necessary.
is a perfect square trinomial.
Take the square root of each side.
Simplify.
Definition of absolute value
Subtract 3 from each side.
Simplify.
Use a calculator to evaluate each value of x. or
Answer: The solution set is {–5.2, –0.8}.

9. Example 2 Find the value of c that makes a perfect square.
Method 1 Use algebra tiles.
is a perfect square.

10. Example 2 cont Method 2 Complete the square. Step 1 Find
Step 2 Square the result of Step 1.
Step 3 Add the result of Step 2 to
Answer:
Notice that

11. Example 3 Solve by completing the square.
Step 1 Isolate the x2 and x terms.
Original equation
Subtract 5 from each side
Simplify.
Step 2 Complete the square and solve.
Since , add 81 to each side.
Factor

12. Example 3 cont Factor Take the square root of each side.
Add 9 to each side.
Simplify. or
Answer: The solution set is {1, 17}.

13. Example 4
Boating Suppose the rate of flow of an 80-foot-wide river is given by the equation where r is the rate in miles per hour, and x is the distance from the shore in feet. Joacquim does not want to paddle his canoe against a current faster than 5 miles per hour. At what distance from the river bank must he paddle in order to avoid a current of 5 miles per hour?
Explore You know the function that relates distance from shore to the rate of the river current. You want to know how far away from the river bank he must paddle to avoid the current.

14. Example 4 cont
Plan Find the distance when Use completing the square to solve
Solve
Equation for the current
Divide each side by –0.01.
Simplify.
Since ½(-80)² = 1600 add 1600 to each side.
Factor

15. Example 4 cont Take the square root of each side. Add 40 to each side
Simplify.
Use a calculator to evaluate each value of x. or
Examine The solutions of the equation are about 7 ft and about 73 ft. The solutions are distances from one shore. Since the river is about 80 ft wide,
Answer: He must stay within about 7 feet of either bank.

16. Summary & Homework Summary: Homework:
Complete the square to make a quadratic function a perfect square
Use the following steps to complete the square of x2 + bx:
Step 1. Find ½ of b, the coefficient of x
Step 2. Square the result of step 1
Step 3. Add the result of step 2 to both sides of the equation
Homework: pg