Question

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

Answer 1

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

Answer 2

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

Answer 3

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)

Answer 4

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.

Answer 5

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

Answer 6

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.

Answer 7

Okay, thank you. I see my problem now!

Answer 8

Great! I'm glad to help! :)