Question

What is the vertex form to standard form?

Answer 1

`y=x^2+2x-2`

Explanation:

Vertex Form:

Vertex form is expressed as:
`y=a(x-h)^2+k`, and is super useful when analyzing the vertex, which is given to be (h, k).

Standard Form:

Standard form is expressed as:
`y=ax^2+bx+c`, and is also useful in certain cases.

Converting Vertex to Standard Form:

When converting standard to vertex we have to complete the square to rewrite the equation using a perfect square binomial, which is what really distinguishes the two. Now when we want to convert back into standard form, we simply need to get rid of this perfect square binomial, which we can do by expanding out the perfect square binomial into a trinomial.

So in other words, we want to multiply out the following:
`(x+1)(x+1)`, which becomes:
`x^2+2x+1` which you can solve by using polynomial multiplication, which is essentially just extending the logic of the distributive property. In general when given two polynomials to multiply, you look at one polynomial, and then multiply it by each term in the other polynomial, now repeat this for each term in the polynomial you were initially looking at. I'll provide a picture to better illustrate this. You can use FOIL if it helps you with multiplying binomials, but remembering how to generally use it, will help you when multiplying polynomials in general.

Now that we've multiplied out the expression, we can substitute it into the equation:
`y=x^2+2x+1-3`, now just combine the constants:
`y=x^2+2x-2`, and now you've converted it into standard form!