How do you write the vertex form equation of the parabola #y=x^2+2x-1#?

1 Answer
Mar 7, 2016

#y+2= (x+1)^2#

Explanation:

Step 1:
Send the constant(-1) to the left by doing,
#y+1=x^2+2x-1+1 rarr y+1=x^2+2x#

Step 2:
Identify the coefficient of #x#
In this case it's #2#

Step 3:
Divide the cofficient by 2.
You get : 2/2 = color(red)1

Step 4:
Add #1# and then subtract #1# from the right.
#y+1=x^2+2x rarr y+1=x^2+2x+ color(red)1-color(red)1#

Step 5:
We see that #x^2+2x+1# can be factorized to the perfect square #(x+1)^2#

#=>y+1=(x+1)^2-1#

Step 6:
Send #-1# to the left by adding #1# to both sides.
#=>y+2=(x+1)^2#

And there you've got the vertex form of the equation of a parabola.

Note:
They call it vertex form simply because it gives us the cordinates of the vertex of the parabola that is being represented.

If we write it like this : #y-(-2)=(x-(-1))^2#
then the vertex can be read as #(-1,-2)#