Question

What is the vertex form of `y= 2x^2+4x-30`?

Answer 1

`y=2(x+1)^2-32`

Explanation:

The vertex form

`y=a(x-h)^2+k` where `(h,k)` is the vertex.

Our question `y=2x^2+4x-30`

We got different approaches for getting to the vertex form.
One is to use the formula for `x`coordinate of the vertex and then using the value to find the `y` coordinate and write the given equation in the vertex form.

We are going to use a different approach. Let us use completing the square.

`y=2x^2+4x-30`

We would first write the given equation in the following way.

`y=(2x^2+4x)-30` As you can see we have grouped the first and the second terms.

`y=2(x^2+2x)-30` Here 2 has been factored out from the grouped term.

Now take the`x` coefficient and divide it by `2`. Square the result. This should be added and subtracted within the parenthesis.

`y=2(x^2+2x+(2/2)^2- (2/2)^2)-30`
`y=2(x^2+2x+1-1)-30`
`y=2(x+1)^2-1)-30` Note `x^2+2x+1 = (x+1)(x+1)`
`y=2(x+1)^2-2-30` Distributed the `2` and removed the parenthesis.

`y=2(x+1)^2-32` The vertex form.