Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
6. Completing the Square
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Exercise 51 Page 238

We want to rewrite the given quadratic equation in vertex form. To do so, we will start by factoring out so the coefficient of will be
We can see that Let's use this to calculate
Simplify
Let's now factor the function by completing the square. We will first add Note that we also have to subtract to leave the function unchanged.
Now we know that the vertex form is Here, we can immediately identify the vertex of the parabola as

Extra

Minimum or Maximum?
What if we wanted to figure out whether the vertex of the function is a minimum value or a maximum value? We would need to look at the value of in the vertex form.
Because is negative, we know that the parabola opens down and the coordinate of the vertex, is the maximum value. Let's graph our function to confirm this conclusion!