# 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

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

#### Explanation:

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