holt algebra 1 9-8 completing the square opener-same sheet-9/21 1.find vertex and describe...
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Holt Algebra 1
9-8 Completing the Square
Opener-SAME SHEET-9/211. Find vertex and describe transformation
a. F(x) = 3(x +2)2 b. f(x) = -(x)2 + 7
2. Find vertex f(x) = -3x2 + 6x
3. Solve by factoring.
a.x2 + 36 = 12x b. 0= x2 – 8x + 12
Holt Algebra 1
9-8 Completing the Square
Factor Practice• X2 – 7x -30=0
• X2 + 4x – 32=0
Holt Algebra 1
9-8 Completing the Square
HW Quiz 9-7(Square Root)Solve using square roots
1. 20x2 = 500
2. X2 = - 400
3. 36x2 = 100
4. 4x2 - 20= 80
Holt Algebra 1
9-8 Completing the Square9-8 Completing the Square
Holt Algebra 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Lesson QuizLesson Quiz
Holt Algebra 1
9-8 Completing the Square
• Find four numbers that make this factorable.
x2 + 8x + ____
Holt Algebra 1
9-8 Completing the Square
Holt Algebra 1
9-8 Completing the Square
Solve quadratic equations by completing the square.
Objective
Holt Algebra 1
9-8 Completing the Square
completing the square
Vocabulary
Holt Algebra 1
9-8 Completing the Square
Opener-SAME SHEET-9/22Solve by finding square root.
• 49x2 + 1 = 170
2. 64x2- 5 = 20
Solve by factoring
3. -2x2 = 18 – 12x
Holt Algebra 1
9-8 Completing the Square
In the previous lesson, you solved quadratic equations by isolating x2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square.
When a trinomial is a perfect square, there is a relationship between the coefficient of the x-term and the constant term.
X2 + 6x + 9 x2 – 8x + 16
Holt Algebra 1
9-8 Completing the Square
An expression in the form x2 + bx is not a perfect square. However, you can use the relationship shown above to add a term to x2 + bx to form a trinomial that is a perfect square. This is called completing the square.
Holt Algebra 1
9-8 Completing the Square
Example 1: Completing the Square
Complete the square to form a perfect square trinomial.
A. x2 + 2x + B. x2 – 6x +
Holt Algebra 1
9-8 Completing the Square
Check It Out! Example 1
Complete the square to form a perfect square trinomial.
a. x2 + 12x + b. x2 – 5x +
Holt Algebra 1
9-8 Completing the Square
To solve a quadratic equation in the form x2 + bx = c, first complete the square of x2 + bx. Then you can solve using square roots.
Holt Algebra 1
9-8 Completing the Square
Solving a Quadratic Equation by Completing the Square
Reading Strategies Wkst
Holt Algebra 1
9-8 Completing the Square
Holt Algebra 1
9-8 Completing the Square
Holt Algebra 1
9-8 Completing the Square
Example 2B: Solving x2 +bx = c
Solve by completing the square.
x2 – 4x – 6 = 0
x = 2 + √10 or x = 2 – √10
Holt Algebra 1
9-8 Completing the Square
Holt Algebra 1
9-8 Completing the Square
Partners
Holt Algebra 1
9-8 Completing the Square
Opener-SAME SHEET-9/22• 1. Solve by completing the square
x2 - 10x + 24 = 0
Holt Algebra 1
9-8 Completing the Square
Opener-SAME SHEET-9/231. Solve by graphing
a. x2 + 5 = 6x b. x2 + 8x +12=0
2. Solve by factoring
a. x2 -2x – 15 = 0 b. x2 + 9x = -14
3. Solve by Sq. Root
a. 5x2 = 320 b. x2 = -16
Holt Algebra 1
9-8 Completing the Square
Check It Out! Example 2b
Solve by completing the square.
t2 – 8t – 5 = 0
Step 6 t = 4 + √21 or t = 4 – √21
Holt Algebra 1
9-8 Completing the Square
Finish Signs
Holt Algebra 1
9-8 Completing the Square
Wkst
Holt Algebra 1
9-8 Completing the Square
Signs
x2 - 10x + 24 = 0
x2 - 6x = –9
x2 + 14x + –26 = 0
2x2 + -4x = 96
2x2 + 14x = 16
Holt Algebra 1
9-8 Completing the Square#7 Type 2 Name
4-24-09
• What does it mean to solve a quadratic equation? Describe how to solve the quadratic equation by completing the square. Use this example to help you explain.
X2 + 14x = 15
SKIP LINES
Holt Algebra 1
9-8 Completing the Square
Example 4: Problem-Solving Application
A rectangular room has an area of 195 square feet. Its width is 2 feet shorter than its length. Find the dimensions of the room. Round to the nearest hundredth of a foot, if necessary.
Holt Algebra 1
9-8 Completing the Square
Example 4 Continued
x = 13 or x = –15
Holt Algebra 1
9-8 Completing the Square
Check It Out! Example 4
An architect designs a rectangular room with an area of 400 ft2. The length is to be 8 ft longer than the width. Find the dimensions of the room. Round your answers to the nearest tenth of a foot.
Holt Algebra 1
9-8 Completing the Square
Check It Out! Example 4 Continued
x 16.4 or x –24.4
Holt Algebra 1
9-8 Completing the Square
Complete the square to form a perfect square trinomial.
1. x2 +11x +
2. x2 – 18x +
Solve by completing the square.
3. x2 – 2x – 1 = 0
4. 3x2 + 6x = 144
5. 4x2 + 44x = 23
Lesson Quiz: Part I
81
6, –8
Holt Algebra 1
9-8 Completing the Square
Lesson Quiz: Part II
6. Dymond is painting a rectangular banner for a football game. She has enough paint to cover 120 ft2. She wants the length of the banner to be 7 ft longer than the width. What dimensions should Dymond use for the banner?
8 feet by 15 feet