 # Section 4 6 Completing the Square Students will

• Slides: 32 Section 4. 6 – Completing the Square Students will be able to: • To solve equations by completing the square • To rewrite functions by completing the square Lesson Vocabulary: Completing the Square Section 4. 6 – Completing the Square Section 4. 6 – Completing the Square Forming a square with model pieces provides a useful geometric image for completing the square algebraically. Essential Understanding: Completing a perfect square trinomial allows you to factor the completed trinomial as the square of a binomial. Section 4. 6 – Completing the Square Problem 1: What is the solution of each equation? 4 x 2 + 10 = 46 Section 4. 6 – Completing the Square Problem 1: What is the solution of each equation? 3 x 2 – 5 = 25 Section 4. 6 – Completing the Square Problem 1: What is the solution of each equation? 7 x 2 – 10 = 25 Section 4. 6 – Completing the Square Problem 1: What is the solution of each equation? 2 x 2 + 9 = 13 Section 4. 6 – Completing the Square Problem 2: While designing a house, an architect used windows like the one shown here. What are the dimensions of the window if it has 2766 square inches of glass? Section 4. 6 – Completing the Square Problem 3: What is the solution of x 2 + 4 x + 4 = 25? Section 4. 6 – Completing the Square Problem 3: What is the solution of x 2 – 14 x + 49 = 25? Section 4. 6 – Completing the Square If x 2 + bx is not part of a perfect square trinomial, you can use the coefficient b to find a constant c so that x 2 + bx + c is a perfect square. When you do this, you are completing the square. Section 4. 6 – Completing the Square When you do this, you are completing the square. Section 4. 6 – Completing the Square When you do this, you are completing the square. Section 4. 6 – Completing the Square Problem 4: What value completes the square for x 2 – 10 x? Justify your answer. Section 4. 6 – Completing the Square Problem 4: What value completes the square for x 2 + 6 x? Justify your answer. Section 4. 6 – Completing the Square Section 4. 6 – Completing the Square Problem 5: What is the solution of 3 x 2 – 12 x + 6 = 0? Section 4. 6 – Completing the Square Problem 5: What is the solution of 2 x 2 – x + 3 = x + 9? Section 4. 6 – Completing the Square You can complete a square to change a quadratic function to vertex form. Problem 6: What is y = x 2 + 4 x – 6 in vertex form? Name the vertex and y-intercept. Section 4. 6 – Completing the Square Problem 6: What is y = x 2 + 3 x – 6 in vertex form? Name the vertex and y-intercept. Section 4. 6 – Completing the Square Problem 6: What is y = 2 x 2 – 6 x – 1 in vertex form? Name the vertex and y-intercept. Section 4. 6 – Completing the Square Problem 6: What is y = -x 2 + 4 x – 1 in vertex form? Name the vertex and y-intercept. Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: x 2 – x = 5 Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: 2 x 2 – ½x = 1/8 Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: 3 x 2 +x = 2/3 Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve the quadratic by completing the square: -. 25 x 2 – 0. 6 x + 0. 3 = 0 Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 2 x 2 – ax = 6 a 2 Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 6 a 2 x 2 – 11 ax = 10 Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 4 a 2 x 2 + 8 ax + 3= 0 Section 4. 6 – Completing the Square EXTRA PROBLEMS: Solve for x in terms of a: 4 a 2 x 2 + 8 ax + 3= 0 Section 4. 6 – Completing the Square Section 4. 6 – Completing the Square