9 8 Completing the Square Objective Solve quadratic
9 -8 Completing the Square Objective Solve quadratic equations by completing the square. Holt Mc. Dougal
9 -8 Completing the Square In the previous lesson, you solved quadratic equations by isolating x 2 and then using square roots. This method works if the quadratic equation, when written in standard form, is a perfect square. When a trinomial is a perfect square, there is a relationship between the coefficient of the x-term and the constant term. X 2 + 6 x + 9 Holt Mc. Dougal x 2 – 8 x + 16 Divide the coefficient of the x-term by 2, then square the result to get the constant term.
9 -8 Completing the Square An expression in the form x 2 + bx is not a perfect square. However, you can use the relationship shown above to add a term to x 2 + bx to form a trinomial that is a perfect square. This is called completing the square. Holt Mc. Dougal
9 -8 Completing the Square Example 1: Completing the Square Complete the square to form a perfect square trinomial. A. x 2 + 2 x + Holt Mc. Dougal B. x 2 – 6 x +
9 -8 Completing the Square Example 2 Complete the square to form a perfect square trinomial. a. x 2 + 12 x + Holt Mc. Dougal b. x 2 – 5 x +
9 -8 Completing the Square To solve a quadratic equation in the form x 2 + bx = c, first complete the square of x 2 + bx. Then you can solve using square roots. Holt Mc. Dougal
9 -8 Completing the Square Solving a Quadratic Equation by Completing the Square Holt Mc. Dougal
9 -8 Completing the Square Example 3 Solve by completing the square. Check your answer. x 2 + 16 x = – 15 Holt Mc. Dougal
9 -8 Completing the Square Example 4 Solve by completing the square. Check your answer. x 2 + 10 x = – 9 Holt Mc. Dougal
9 -8 Completing the Square Practice Complete the square to form a perfect square trinomial. 1. x 2 +11 x + 2. x 2 – 18 x + Solve by completing the square. 3. x 2 + 6 x = 144 4. x 2 + 8 x = 23 Holt Mc. Dougal
- Slides: 10