**Q:** What is completing the square?

**A:** Completing the square is a technique used to convert from general form, , to standard form, . Why do we need to convert? Standard form is much easier to graph as a parabola.

Let’s look at some examples:

Write each function in the form

**a)**

*Step 1:* Take half of the **b** term (in this case, b=10) and square it.

*Step 2:* Add that number to the equation, but then subtract it from the end of the equation. Why? So that you are actually just adding **0** to the equation.

*Step 3:* You now have a perfect square (because 5+5=10, and 5*5=25), so group those terms together and factor:

**This is a parabola in standard form
with a=1, and the vertex is at (p,q)=(-5,5).**

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