Answer:
See Below.
Step-by-step explanation:
To convert a quadratic in standard form to vertex form, we will complete the square.
Let’s say we have a quadratic in standard form:
To start, we will factor the leading coefficient from the first two terms:
Next, we will divide the coefficient of the second term by 2, square it, and then add it to our equation.
Our coefficient of the second term is b/a. b/a divided by 2 is b/2a. And squaring yields b²/4a². So:
Of couse, we will also need to subtract it as well to keep our equation equal.
Since a is being distributed, we will subtract a(b²/4a²) or b²/4a. So:
Finally, we can use the perfect trinomial pattern to factor. So:
And this is vertex form.
Let’s see this with an example. Say we have:
And we want to convert this to vertex form.
As above, factor out the leading coefficient from the first two terms:
Divide the coefficent of the second term by 2 and then square it.
2/2 is 1. 1 squared is still 1.
So, we will add 1 within our parentheses:
Since we added 1 <em>inside</em>, we must <em>subtract</em> 2(1) outside. So:
Now, we can factor. Therefore:
And this is in vertex form.