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**2-4 completing the square**

Chapter 2 2-4 completing the square

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**objectives *Solve quadratic equations by using the square property**

* Solve quadratic equations by completing the square.

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Square root property Many quadratic equations contain expressions that cannot be easily factored. For equations containing these types of expressions, you can use square roots to find roots.

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**Examples using the square root property**

Example #1 Solve the equation. 4 𝑥 2 +11=59 Solution: 4 𝑥 2 +11=59 solve for x −11 −11 4 𝑥 2 =48 4 𝑥 2 4 = 48 4 𝑥 2 =12 𝑥= 12

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Example #2 Solve the equation. x2 + 12x + 36 = 28

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**Student Guided Practice**

Solve the following equations 1. 4x2 – 20 = 5 2. x2 + 8x + 16 = 49

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**Completing the square What is completing the square? Answer:**

If a quadratic expression of the form x2 + bx cannot model a square, you can add a term to form a perfect square trinomial. This is called completing the square.

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Completing the square

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**Completing the square steps**

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Example #3 Solve the equation by completing the square. x2 = 12x – 20

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Example#4 Solve the equation by completing the square 18x + 3x2 = 45

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**Example #5 Solve each equation by completing the square.**

1) problem #1 in completing the square worksheet p2 + 14p − 38 = 0

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**Student guided practice**

Do problems from worksheet 2-6 and

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**Writing quadratic functions in vertex form**

Recall the vertex form of a quadratic function from lesson: f(x) = a(x – h)2 + k, where the vertex is (h, k). You can complete the square to rewrite any quadratic function in vertex form.

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**Example #6 Write the function in vertex form, and identify its vertex.**

f(x) = x2 + 16x – 12

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**Example#7 Write the function in vertex form, and identify its vertex**

g(x) = 3x2 – 18x + 7

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**Student guided practice**

Write the function in vertex form, and identify its vertex g(x) = 3x2 – 18x + 7

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homework Do problems 26 through 36 From page 89

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Closure Today we learn about solving a quadratic equation using completing the square. Next class we are going to learn about complex numbers and roots

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