# 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?

Nov 5, 2015

Let's expand the second function:

$y = 2 \left({x}^{2} - 8 x + 16\right) + 3 x - 12 - 4$

$= 2 {x}^{2} - 16 x + 32 + 3 x - 16$

$= 2 {x}^{2} - 13 x + 16$

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

Blue graph is $y = 2 {x}^{2} + 3 x - 4$
It takes the y-value you would have obtained on the blue graph at its $\left(x - 4\right)$ 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