Plot the graph of the equation x = y² - 3?

Question

how do I get started and finish the problem correctly?

Answer 1

You recognize equations in the form y=..., so move the three over:
y^2=x+3
and take the square root (but remember, it can be positive or negative):
y=+/- sqrt(x+3)
Now you can plot that.

Answer 2

A good way to answer questions like these is to make a chart. Set values for Y, (begin with a value such as -3, and then do intervals of 1 or 2 numbers), and then plug in this Y value, so get your corresponding X value:

Y^2 - 3 = X

Y= -3 --> [(-3)^2] - 3 = X = 6
So, your first value would be (6,-3)

Y = -1 --> [(-1)^2]-3 = X = -2
Your second value would be (-2,-1)

Y = 1 --> (1^2) - 3 = X = -2
Your thrid value would be (-2,1)

Y = 3 --> (3^2) - 3 = X = 6
Your forth point would be (6,3)

If you plot these points, you will see that the graph will be a parabola with symmetry over the X axis.

Good luck with it!

Answer 3

Give some values to obtain some points:-
x |- 3____0_____6______9_______12
y | 0___±√3____±3____±2√3_____±√15

Curve may be sketched using these points.
Will be a "horizontal" parabola with vertex (-3 , 0)
Axis of symmetry is x axis.

Answer 4

if x=y square-3,
y square=x+3
assume x=1 so,y=2
if x=6,y=3
so,(1,2) and (6,3)
plot it on the graph.