Lesson Completing the Square

The purpose of this lesson is to demonstrate how to write a quadratic equation in vertex form using the completing the square method.
Given a standard quadratic equation:

End result in vertex form:

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The basis of the completing the square method is the relationship between the squared binomial and its resulting trinomial.
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Working backwards, notice that a is half of 2a.
For example, given , we know that half of 8 is 4 and 4² is 16
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Now lets say you have what do i need to add to make it a perfect square?
Well half of (-2) is (-1) and (-1)² is 1. Therefore, by adding 1 it becomes a perfect square.
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I will demonstrate the entire process step-by-step using the following example:

Step 1: Group the first 2 terms together, separating them from the constant term.
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Step 2: Factor out leading coefficient, for completing the square to work, the coefficient of x² must be 1.
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Step 3: Complete the square, Take half of x coefficient and square it. Notice to keep equation balanced you must add this number and subtract it making the net effect zero.
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Step 4: Distribute and add constants
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Now it is successfully in vertex form and can be easily graphed.
The vertex is at (-3,-25)
The parabola opens up and has a y-intercept at (0, -7)
Here is a graph of this parabola: