Simplify each expression.

Slides:

Advertisements

Similar presentations

Section 5.7 Completing the Square.

Advertisements

5-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Read as “plus or minus square root of a.”

+ Completing the Square. + In your notes: Simplify the following: (5 – 3i)(4 + 2i) 3.

4.7 – Complete the Square In lesson 4.5, you solved equations of the form x2 = k by finding the square roots. This method also works if one side of an.

5-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

CH. 8.6 Natural Logarithms. Write 2 ln 12 – ln 9 as a single natural logarithm. 2 ln 12 – ln 9 = ln 12 2 – ln 9Power Property = lnQuotient Property 12.

Solving Quadratics by Completing the Square, continued Holt Chapter 5 Section 4.

U4L3 Solving Quadratic Equations by Completing the Square.

Holt McDougal Algebra Completing the Square Solve quadratic equations by completing the square. Write quadratic equations in vertex form. Objectives.

Objectives Solve quadratic equations by completing the square.

Solve x x + 49 = 64 by using the Square Root Property.

Completing the Square 4-6 Day 1 Today’s Objective: I can use the process of completing the square to solve or rewrite a quadratic equation.

Factoring Polynomials by Completing the Square. Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x x + 25 l x x + 36.

Solving by Completing the Square What value would c have to be to make the following a perfect square trinomial?

Why we complete the square  We have learned how to factor quadratic expressions to solve.  Many quadratic equations contain expressions that cannot be.

Properties of Real Numbers Objective: To add, subtract, multiply and divide real numbers and to use the Distributive Property.

Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.

Factoring Polynomials.

Solving Inequalities Using Addition and Subtraction

Algebra Completing the Square. Solving with Square Roots.

2-4 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Chapter 4: Quadratic Functions and Equations

Solve Quadratic Equations by Completing the Square

(x – 6)2 = 9 Factor the trinomial.

Solving Quadratic Equations by Completing the Square

Many quadratic equations contain expressions that cannot be easily factored. For equations containing these types of expressions, you can use square roots.

Objectives Solve quadratic equations by completing the square.

Solving Quadratic Equations by Completing the Square

Section 3.3 Beginning on page 112

Solving Quadratic Equations by Completing the Square

EXAMPLE 2 Rationalize denominators of fractions Simplify

4.6 Completing the Square Learning goals

4.6 Completing the Square Learning goals

Solving Quadratic Equations by Completing the Square

Completing the Square (3.2.3)

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Chapter 6.4 Completing the Square Standard & Honors

Solving Quadratic Equations by Completing the Square

Algebra 2 Ch.5 Notes Page 37 P Completing the Square.

Solving Quadratic Equations by Completing the Square

Section 9.4 Day 1 Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Section 9.4 Day 1 Solving Quadratic Equations by Completing the Square

You can find the roots of some quadratic equations by factoring and applying the Zero Product Property. Functions have zeros or x-intercepts. Equations.

Solving Multi-Step Equations

8-8 Completing the Square Warm Up Lesson Presentation Lesson Quiz

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Completing the Square Algebra Review.

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

The constant is always the square of half Or

13.3 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Warm-Up Set 1: Factor. 1) x2 + 6x + 9 2) x2 - 10x + 25 Set 2: Factor.

6-3 Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Presentation transcript:

Simplify each expression. Completing the Square ALGEBRA 2 LESSON 5-7 (For help, go to Lessons 5-1 and page 262.) 9 16 1. (x – 3)(x – 3) 2. (2x – 1)(2x – 1) 3. (x + 4)(x + 4) – 3 4. ± 25 5. ± 48 6. ± –4 7. ± Simplify each expression. 5-7

1. (x – 3)(x – 3) = x2 – 2(3)x + 32 = x2 – 6x + 9 Completing the Square ALGEBRA 2 LESSON 5-7 Solutions 9 16 3 4 1. (x – 3)(x – 3) = x2 – 2(3)x + 32 = x2 – 6x + 9 2. (2x – 1)(2x – 1) = (2x)2 – 2(1)(2x) + 12 = 4x2 – 4x + 1 3. (x + 4)(x + 4) – 3 = x2 + 2(4)x + 42 – 3 = x2 + 8x + 16 – 3 = x2 + 8x + 13 4. ± 25 = ±5 5. ± 48 = ± 16 • 3 = ±4 3 6. ± –4 = ± –1 • 4 = ±2i 7. ± = ± = ± 5-7

(x – 6)2 = 9 Factor the trinomial. Completing the Square ALGEBRA 2 LESSON 5-7 Solve x2 – 12x + 36 = 9. x2 – 12x + 36 = 9 (x – 6)2 = 9 Factor the trinomial. x – 6 = ±3 Find the square root of each side. x – 6 = 3 or x – 6 = –3 Solve for x. x = 9 or x = 3 5-7

Find the missing value to complete the square: x2 + 20x + . Completing the Square ALGEBRA 2 LESSON 5-7 Find the missing value to complete the square: x2 + 20x + . = = 100 Find . Substitute 20 for b. b 2 20 x2 + 20x + 100 Complete the square. 5-7

x2 + 4x = –1 Rewrite so all terms containing x are on one side. Completing the Square ALGEBRA 2 LESSON 5-7 Solve x2 + 4x + 1 = 0. = 4 Find . 4 2 b x2 + 4x = –1 Rewrite so all terms containing x are on one side. x2 + 4x + 4 = –1 + 4 Complete the square by adding 4 to each side. (x + 2)2 = 3 Factor the perfect square trinomal. x + 2 = ± 3 Find the square root of each side. x = –2 ± 3 Solve for x. 5-7

Completing the Square (continued) Check: ALGEBRA 2 LESSON 5-7 (continued) Check: (–2)2 – 2(–2 3) + ( 3)2 – 8 – 4 3 + 1 (–2 + 3)2 + 4(–2 + 3) + 1 x2 + 4x + 1 0 = 0 4 – 4 3 + 3 – 8 + 4 3 + 1 (4 + 3 – 8 + 1) + (–4 3 + 4 3) (–2)2 + 2(–2 3) + ( 3)2 + (–8) + 4 3 + 1 (–2 – 3)2 + 4(–2 – 3) + 1 4 + 4 3 + 3 – 8 – 4 3 + 1 (4 + 3 – 8 + 1) + (4 3 – 4 3) 5-7

Rewrite so all terms containing x are on one side. Completing the Square ALGEBRA 2 LESSON 5-7 Solve x2 + 6x + 12 = 0. 6 2 b = 9 Find . x2 + 6x = –12 Rewrite so all terms containing x are on one side. x2 + 6x + 9 = –12 + 9 Complete the square by adding 9 to each side. (x + 3)2 = –3 Factor the perfect square trinomial. x + 3 = ± –3 Find the square root of each side. x = –3 ± –3 Solve for x. = –3 ± i 3 Simplify. 5-7

= Completing the Square Solve 2x2 + 7x – 1 = 0. x2 + x – = 0 ALGEBRA 2 LESSON 5-7 Solve 2x2 + 7x – 1 = 0. x2 + x – = 0 7 2 1 Divide each side by 2. x2 + x = 1 2 7 Rewrite so all terms containing x are on one side. = 7 2 49 16 Find . b x2 + x + = + 7 2 49 16 1 Complete the square by adding to each side. x + = 7 4 57 16 Factor the perfect square trinomial. 2 7 4 57 x + = ± Find the square root of each side. x = – ± 7 4 Solve for x. 57 5-7

Write y = x2 + 5x + 2 in vertex form. Completing the Square ALGEBRA 2 LESSON 5-7 Write y = x2 + 5x + 2 in vertex form. y = x2 + 5x + 2 = x2 + 5x + + 2 – 5 2 Complete the square. Add and subtract on the right side. = x + + 2 – 25 4 5 2 Factor the perfect square trinomial. = x + – 5 2 17 4 Simplify. The vertex form is y = x + – . 5 2 17 4 5-7

Homework P. 281 # 13 – 33 eoo