Chapter 6.4 Completing the Square Standard & Honors Algebra II Mr. Gilbert Chapter 6.4 Completing the Square Standard & Honors 11/19/2018

Agenda Warm up Homework Check your answers Lesson 11/19/2018

Topic: Completing the Square Example 1 Equation with Rational Roots (2) Example 2 Equation with Irrational Roots (4) Example 3 Complete the Square (3) Example 4 Solve an Equation by Completing the Square (3) Example 5 Equation with a  1 (3) Example 6 Equation with Complex Solutions (4) You will need a graphing calculator for this section. 11/19/2018 Lesson 4 Contents

Solve by using the Square Root Property. Original equation Factor the perfect square trinomial. Square Root Property Subtract 7 from each side. Write as two equations. or Solve each equation. Answer: The solution set is {–15, 1}. 11/19/2018 Example 4-1a

Solve by using the Square Root Property. Answer: {3, 13} 11/19/2018 Example 4-1b

Solve by using the Square Root Property. Original equation Factor the perfect square trinomial. Square Root Property Add 5 to each side. Write as two equations. or 11/19/2018 Example 4-2a

Subtract 12 from each side. Answer: The exact solutions of this equation are and The approximate solutions are 1.5 and 8.5. Check these results by finding and graphing the related quadratic function. Original equation Subtract 12 from each side. Related quadratic function 11/19/2018 Example 4-2a

Check Use the ZERO function of a graphing calculator Check Use the ZERO function of a graphing calculator. The approximate zeros of the related function are 1.5 and 8.5. 11/19/2018 Example 4-2a

Solve by using the Square Root Property. Answer: 11/19/2018 Example 4-2b

Step 2 Square the result of Step 1. Find the value of c that makes a perfect square. Then write the trinomial as a perfect square. Step 1 Find one half of 16. Step 2 Square the result of Step 1. Step 3 Add the result of Step 2 to Answer: The trinomial can be written as 11/19/2018 Example 4-3a

Find the value of c that makes. a perfect square Find the value of c that makes a perfect square. Then write the trinomial as a perfect square. Answer: 9; (x + 3)2 11/19/2018 Example 4-3b

Solve by completing the square. Notice that is not a perfect square. Rewrite so the left side is of the form Since add 4 to each side. Write the left side as a perfect square by factoring. 11/19/2018 Example 4-4a

Subtract 2 from each side. Square Root Property Subtract 2 from each side. Write as two equations. or Solve each equation. Answer: The solution set is {–6, 2}. 11/19/2018 Example 4-4a

Solve by completing the square. Answer: {–6, 1} 11/19/2018 Example 4-4b

Solve by completing the square. Notice that is not a perfect square. Divide by the coefficient of the quadratic term, 3. Add to each side. Since add to each side. 11/19/2018 Example 4-5a

Write the left side as a perfect square by factoring Write the left side as a perfect square by factoring. Simplify the right side. Square Root Property Add to each side. 11/19/2018 Example 4-5a

Answer: The solution set is Write as two equations. or Solve each equation. Answer: The solution set is 11/19/2018 Example 4-5a

Solve by completing the square. Answer: 11/19/2018 Example 4-5b

Solve by completing the square. Notice that is not a perfect square. Rewrite so the left side is of the form Since add 1 to each side. Write the left side as a perfect square by factoring. 11/19/2018 Example 4-6a

Subtract 1 from each side. Square Root Property Subtract 1 from each side. Answer: The solution set is Notice that these are imaginary solutions. 11/19/2018 Example 4-6a

Check. A graph of the related function shows that the Check A graph of the related function shows that the equation has no real solutions since the graph has no x-intercepts. Imaginary solutions must be checked algebraically by substituting them in the original equation. 11/19/2018 Example 4-6a

Solve by completing the square. Answer: 11/19/2018 Example 4-6b

11/19/2018 End of Lesson 4

Homework Review 11/19/2018

Homework - Honors See Syllabus 6.4 Pg 311 25-48 multiples of 3, 49,50,52 11/19/2018

Homework See Syllabus 6.4 Pg 311 25-47 odd 11/19/2018