The answer is b. can you me tho do i have to plug in the coordinates?

Plugging in your coordinates gives you a few points that match up with the given graph, yes!!

you could solve this a few ways, through trial and error of plugging in small numbers like 0, 1, -1, and so on into the equations until you get points that match up.

you could take the graph and just judge it by looking, too. if you know what a basic parabola looks like, y = x^2, and if you know how it transforms, then you can rule the other ones out.

A. the +2 would move the parabola two units to the right, which would take the vertex away from (0, 0). because your given graph HAS a vertex of (0, 0), this one is immediately out.

when x = 0...
y = (0)^2 + 2
y = 2

(0, 2) is NOT consistent with your graph. plugging in a point takes it out as well.

C. if the base equation is y = x^2, putting a negative in front simply turns the parabola down. it would look like a frown instead of an upward smile.

when x = 0...
y = -(0)^2
y = 0

(0, 0)

by plugging in, you get one point correct; the vertex. try 1.

when x = 1...
y = -(1)^2
y = -1

(0, -1) does NOT match your graph. that one is out, too.

D. if a parabola has a fraction in front of it, it's makes the parabola wider. the one on your graph is rather thin, so you can rule it out based on visuals.

when x = 0...
y = (1/2)(0)^2
y = 0

(0, 0)

this one is the same on the first point too. if you plug in another, though:

when x = 1
y = (1/2)(1)^2
y = 1/2

(1, 1/2) does NOT match your graph, so it's out as well.

i hope this like helps even tho it's long