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.
