Question

Complete the statements below that show y = x2 + 2x - 1 being converted to vertex form

Answer 1

Vertex form should be : y = (x+1)^2 - 2, where the vertex is (-1,-2)

Answer 2

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

Explanation:

General polynomial formula of a quadratic equation

`ax^2+bx+c`

Equation
`y= x^2+2x-1`

`a= 1\\ b=2\\ c=-1`

The formula to find the x coordinate of the vertex is

`V_(x)= (-b)/(2a)`

`V_(x)=(-2)/(2(1)) \\ V_(x)= -1`

Now to find the y coordinate of the vertex we substitute the found value of the x coordinate in
`y= x^2+2x-1`

`y= (-1)^2+2(-1)-1 \\ y= 1-2-1\\ y=-2`

The general vertex formula for any quadratic function is

`y= a(x-x_(v))^2+y_(v)`

Replace

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