5 4 completing the square and solving by square root method
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5.4 Completing the Square and Solving by Square Root Method PowerPoint PPT Presentation


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ax 2 + bx + c = 0. Sometimes it is easier to solve a quadratic equation by using a different method other than factoring. Sometimes you cannot even solve the quadratic equation by factoring. Objectives. 5.4 Completing the Square and Solving by Square Root Method.

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5.4 Completing the Square and Solving by Square Root Method

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5 4 completing the square and solving by square root method

ax2 + bx + c = 0

Sometimes it is easier to solve a quadratic equation by using a different method other than factoring. Sometimes you cannot even solve the quadratic equation by factoring.

Objectives

5.4 Completing the Square and Solving by Square Root Method

Solve quadratic equations by taking the square root of both sides

Solve quadratic equations by completing the square.

Write quadratic equations in vertex form.

Vocabulary

completing the square


5 4 completing the square and solving by square root method

We have learned to solve quadratic equations by factoring:

x2 + 16 = 0

Can you think of a easier method for solving the quadratic equation?


5 4 completing the square and solving by square root method

Example 1A: Solving Equations by Using the Square Root Property

Solve the equation.

4x2 + 11 = 59


5 4 completing the square and solving by square root method

Solving quadratic equations by factoring:

x2 + 7x-8 = 0

x2 + 8x +16 = 0


5 4 completing the square and solving by square root method

Example: Solve the equation by completing the square.

x2= 12x – 20


5 4 completing the square and solving by square root method

Example: Solve the equation by completing the square.

18x + 3x2 = 45


5 4 completing the square and solving by square root method

Helpful Hint

In Example 3, the equation was balanced by adding to both sides. Here, the equation is balanced by adding and subtracting on one side.

Recall the vertex form of a quadratic function from lesson 5-1:

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.


5 4 completing the square and solving by square root method

Example 4A: Writing a Quadratic Function in Vertex Form

Write the function in vertex form, and identify its vertex.

f(x) = x2 + 16x – 12


5 4 completing the square and solving by square root method

Example 4B: Writing a Quadratic Function in Vertex Form

Write the function in vertex form, and identify its vertex

g(x) = 3x2 – 18x + 7


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