In this lesson, we're going to talk about how to convert a quadratic function in standard form to vertex form and vice versa. Sometimes you may need to be able to do this, so let's cover it in this video. And the way to do it is to use the...
we need to complete a square, basically. Half of 6 is 3, so we're going to add 3 squared to both sides. Adding it to the left side is the same as subtracting it from the right side. So we can add 3 squared to both sides, or we can add 9 to the right side.
right side and also simultaneously subtract 9 from the right side. 9 and negative 9 is 0 so we're not changing the value of the right side. So let's do it that way. Now let's factor x squared plus 6x plus 3 squared. Every time you complete the square, you're creating a perfect square trinomial.
And to factor it, you can see everything you need here. First it's x. Then, whatever this sign is, it's plus, and then it's this number before you square it, 3 squared.
Outside, we have negative 5 minus 9. So in vertex form, it's x plus 3 squared. minus 14. So we can clearly see that the vertex is negative 3, negative 14. And we can also use this equation to find vertex, negative b over 2a. b is 6, a is 1, negative 6 over 2 is negative 3, which confirms the x value here.
Now let's talk about how we can go back to standard form. So how can we convert this expression, which is in vertex form, back to standard form? All you need to do is expand x plus 3 squared.
Let's FOIL it. x times x is x squared. x times 3 is 3x.
3 times x is 3x. 3 times 3 is 9. and then combine like terms. 3x plus 3x is 6x. 9 minus 14 is negative 5. So this gives us the original function in standard form.
So now you know how to convert from standard form to vertex form by completing the square. And you know how to convert from vertex form to standard form by expanding and using the FOIL method.