# How do you convert #y=x^2-2x+3 # in vertex form?

##### 1 Answer

Please see the explanation.

#### Explanation:

The vertex form of a parabola that opens up or down is:

where "a" is the same as the "a" in the standard form for a parabola that opens up or down:

To convert to the vertex form, add 0 in the form of #ah^2 - ah^2 to the equation:

Factor out "a" from the first 3 terms:

Using the pattern (x - h)^2 = x^2 - 2hx + h^2, observe that middle term of the pattern equals the middle term of the equation:

Solve for h:

Substitute the left side of the pattern into the equation:

Substitute

In a problem with numbers, the last step is to combine the constant terms.

Given:

Substitute the left side of the pattern into the equation:

Substitute 1 for h:

Combine the constant terms: