MATHEMATICS

QUADRATIC FUNCTIONS: Completing the Square

If a is 3x, then what's b? It's not the same 3x as in the original equation! Remember, we're comparing it to a^2 + 2ab. So

We can find b by dividing 2ab by 2a.

Next we input a and b into the (Ax + B)^2. We're still only looking at what's inside the brackets. 

Let's see what happens when we expand (Ax + B)^2.

The first two terms look about right, but there's a third term, equivalent to b^2, that's not present in our original quadratic equation. We can keep the value of the equation – that is, the first two terms - the same if we just subtract b^2 from the final product.

The expression can be condensed back into

Finally, let's bring back that last + 1 that we excluded. It tags on the end of the expression like this

And we can add the subtracted b^2 to it to find C, giving us our completed expression.

Try expanding it and see if you get the same equation we started out with!

(I've reached my 20-image limit, so click the next part to continue.)