Algebra II Mr Gilbert Chapter 6 4 Completing

Algebra II Mr. Gilbert Chapter 6. 4 Completing the Square Standard & Honors 12/16/2021 1

Agenda Warm up u Homework u – Check your answers u 12/16/2021 Lesson 2

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. 12/16/2021 3

Solve Root Property. by using the Square Original equation Factor the perfect square trinomial. Square Root Property Subtract 7 from each side. or Write as two equations. Solve each equation. Answer: The solution set is {– 15, 1}. 12/16/2021 4

Solve Root Property. by using the Square Answer: {3, 13} 12/16/2021 5

Solve Root Property. by using the Square Original equation Factor the perfect square trinomial. Square Root Property Add 5 to each side. or 12/16/2021 Write as two equations. 6

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 12/16/2021 7

Check Use the ZERO function of a graphing calculator. The approximate zeros of the related function are 1. 5 and 8. 5. 12/16/2021 8

Solve Root Property. by using the Square Answer: 12/16/2021 9

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 as 12/16/2021 can be written 10

Find the value of c that makes a perfect square. Then write the trinomial as a perfect square. Answer: 9; (x + 3)2 12/16/2021 11

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. 12/16/2021 12

Square Root Property Subtract 2 from each side. Write as two equations. or Solve each equation. Answer: The solution set is {– 6, 2}. 12/16/2021 13

Solve by completing the square. Answer: {– 6, 1} 12/16/2021 14

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 12/16/2021 15 to each side.

Write the left side as a perfect square by factoring. Simplify the right side. Square Root Property Add 12/16/2021 16 to each side.

Write as two equations. or Solve each equation. Answer: The solution set is 12/16/2021 17

Solve by completing the square. Answer: 12/16/2021 18

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. 12/16/2021 19

Square Root Property Subtract 1 from each side. Answer: The solution set is Notice that these are imaginary solutions. 12/16/2021 20

Check 12/16/2021 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. 21

Solve by completing the square. Answer: 12/16/2021 22

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Homework Review 12/16/2021 24

Homework - Honors See Syllabus 6. 4 Pg 311 25 -48 multiples of 3, 49, 50, 52 12/16/2021 25

Homework See Syllabus 6. 4 Pg 311 25 -47 odd 12/16/2021 26