## kylewendt one year ago What is the graph to 2x^2=8? I know this is a standard parabola, but what do you do with the 8?

1. dg98

are you sure it's a graph? shouldn't it always be equal to y or f(x)?

2. kylewendt

Yes, it is a graph. If you need me to, I can copy the exact question (Which isn't much different)

3. AccessDenied

If we graph y = 2x^2 and y = 8 individually, their intersection is the graph for that equation; That said, 2x^2 is indeed a parabola with a bit of vertical stretch. The 8 is a constant. Consider it as a class of points where the y-value is 8: (x, 8) We can put any x-value in and get a point on this line, so the line is just a horizontal line through (0, 8)

4. AccessDenied

Or alternatively, I think you could bring that 8 over to the left: 2x^2 - 8 = 0 and draw that graph, which is the same parabola but shifted downwards by 8 units. The intersection at y=0 is the solution set in that case.

5. kylewendt

So, with 2 solutions, -2 and 2, would this be the graph?

6. AccessDenied

That parabola seems to be flipped upside-down, implying it has a negative leading coefficient and positive vertical shift upwards. This parabola given by the equation has to be facing up because its leading term is +2. The whole graph will be shifted down 8 units.

7. kylewendt

Okay, thank you. I see my problem now!

8. AccessDenied

Great! I'm glad to help! :)