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
