Section 4 5 Notes Completing the Square Example

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Section 4. 5 Notes: Completing the Square

Section 4. 5 Notes: Completing the Square

Example 1: Solve x 2 + 14 x + 49 = 17 by using

Example 1: Solve x 2 + 14 x + 49 = 17 by using the Square Root Property.

Example 2: Solve x 2 – 4 x + 4 = 13 by using

Example 2: Solve x 2 – 4 x + 4 = 13 by using the Square Root Property.

All quadratic equations can be solved using the Square Root Property by manipulating the

All quadratic equations can be solved using the Square Root Property by manipulating the equation until one side is a perfect square. This method is called completing the square.

Example 3: Find the value of c that makes x 2 + 12 x

Example 3: Find the value of c that makes x 2 + 12 x + c a perfect square. Then write the trinomial as a perfect square.

You can solve any quadratic equation by completing the square. Because you are solving

You can solve any quadratic equation by completing the square. Because you are solving an equation, add the value you use to complete the square to EACH side. BUT 1 st move your given c value, so you can find your own like the last example! Example 4: Solve x 2 + 4 x – 22 = 0 by completing the square.

We cannot complete the square when “a” does not equal 1. How can we

We cannot complete the square when “a” does not equal 1. How can we make the 3 go away in the next example? Example 5: Solve 3 x 2 – 6 x + 12 = 0 by completing the square.

Example 6: Solve x 2 + 4 x + 11 = 0 by completing

Example 6: Solve x 2 + 4 x + 11 = 0 by completing the square.

When a quadratic function is in the form y = ax 2 + bx

When a quadratic function is in the form y = ax 2 + bx + c, you can complete the square to write the function in vertex form. However, the easier method is to find the vertex (h, k) from your calculator, and then plug a, h and k into the equation y = a(x – h)2 + k Example 7: Write each function in Vertex Form. a) y = x 2 – 2 x + 4 b) y = x 2 + 4 x + 6

Example 7 cont. : Write each function in Vertex Form. c) y = –

Example 7 cont. : Write each function in Vertex Form. c) y = – 3 x 2 – 18 x + 10 d) y = 2 x 2 – 12 x + 17