4.7: Completing the Square Page 95 13. 15. 17. 19. 21. 23. 41. 2 Reals, Discriminant: 12 43. 2 Reals, Discriminant: 180 45. 1 Double Root, Discriminant: 0 A. +16 B. c < –100 4/23/2019 8:58 PM 4.7: Completing the Square 1

Section 2.2 Revised ©2011, viet.dang@humble.k12.tx.us Completing the Square Section 2.2 Revised ©2011, viet.dang@humble.k12.tx.us 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Steps Put terms with variables on one side and CONSTANT to the other side Make sure the side is in DESCENDING order Standard Form, Ax2 + Bx + C = 0 where A = 1 Identify the coefficient which is raised to the first power, DIVIDE the term by 2, and SQUARE the number (it will always be positive) ADD to both sides to the equation Put the equation into FACTORED form (Vertex Form) SQUARE ROOT both sides and cancel the binomial Solve for x and check 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 1 Solve x2 – 4x + 3 = 0 using completing the square Step 1: Put terms with variables on one side and terms without variables onto other side Make sure the side is in DESCENDING order Standard Form, Ax2 + Bx + C = 0 where A = 1 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 1 Solve x2 – 4x + 3 = 0 using completing the square Step 2: Identify the coefficient which is raised to the first power and divide the term by 2 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 1 Solve x2 – 4x + 3 = 0 using completing the square Step 3: Take the second term, divide the term by 2, and square that number 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 1 Solve x2 – 4x + 3 = 0 using completing the square Step 4: Add to both sides to the equation 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 1 Solve x2 – 4x + 3 = 0 using completing the square Step 5: Put the equation into factored form (Vertex Form) 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 1 Solve x2 – 4x + 3 = 0 using completing the square Step 6: Square Root both sides and cancel the binomial 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 1 Solve x2 – 4x + 3 = 0 using completing the square Step 7: Solve and Check 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 2 Solve x2 – 24x + 144 = 100 using completing the square 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Your Turn Solve x2 = 12x – 20 using completing the square 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 3 Solve x2 – 4x = –2 using completing the square 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 4 Solve 2x2 + 12x – 32 = 0 using completing the square 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 5 Solve 2x2 – 6x = 5 using completing the square 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Your Turn Solve –6x + 2x2 = –1 using completing the square 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Vertex Form Equation: y = a(x – h)2 + k The vertex is (h, k). Think of HONG KONG a is the scalar. FOIL the problem out. Don’t forget to multiply the scalar and factors. REMINDER: To complete the square, the leading coefficient must be 1. Since the h and k are on the same side, you will take ½ of b, square it, add to the first part and SUBTRACT from the k. 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 6 Given x2 + 4x = 5, convert to Vertex Form 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 7 Given x2 – 4x = –13, convert to Vertex Form 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Your Turn Given x2 – 16x = –2, convert to Vertex Form 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 8 Given y = 2x2 – 8x + 3, convert to Vertex Form 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 9 Given 9x2 + 18x = –3, convert to Vertex Form 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Your Turn Given 2x2 + 25 = –6x, convert to Vertex Form 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 10 Write a rule in transformation form for the quadratic function with the vertex is at the origin and passes through (2, 12). 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Example 11 Write a rule in transformation form for the quadratic function with the vertex is at the (5, 2) and passes through (4, 5). 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Your Turn Write a rule in transformation form for the quadratic function with the vertex is at the (2, –5) and passes through (3, –11). 4/23/2019 8:58 PM 4.7: Completing the Square

4.7: Completing the Square Assignment Worksheet 4/23/2019 8:58 PM 4.7: Completing the Square