What is the difference between the graph of #y=2x^2+3x-4# and the graph of #y=2(x-4)^2+3(x-4)-4#?

2 Answers
Nov 5, 2015

Let's expand the second function:

#y=2(x^2-8x+16)+3x-12-4#

#= 2x^2-16x+32+3x-16#

#= 2x^2 -13 x + 16#

So, both functions are quadratic polynomials, and then in both cases you have a parabola, and since the #x^2# coefficients are both positive (they are both #2#), they are both #cup#-shaped, instead of #cap#-shaped.

I wouldn't know what to add, they are simply two different parabolas, what did you mean with "what is the difference between" them?

Nov 5, 2015

Answer:

The difference between them is that one is a duplicate of the other but has been shifted to the right by 4

Explanation:

enter image source here

Blue graph is #y=2x^2+3x-4#

It takes the y-value you would have obtained on the blue graph at its #(x-4)# and plotted it at #x#. The consequence of this is as though the whole thing has been 'shunted' to the right on the x-axis by 4