Question

Determine whether the equation has a graph that is symmetric with respect to the y-axis, the x-axis, the origin, or
none of these.
1) x2 - y2 = 4
2) y = -5x3 + 4x

Instead of just the answer I'd like explanation too, please and thank you

Answer 1

1)
Note that when x = 2 y = 0
and when x = -2 y = 0

Answer 2

what might this suggest?

Answer 3

also there are 2 squared variables which suggests a type of conic section ( ellipse or hyperbole)

Answer 4

elipse? since they are even numbers?

Answer 5

No - it has a negative sign so its a hyperbole
and its symmetrical about which axis?

Answer 6

oh y-axis

Answer 7

correct

Answer 8

2) is a cubic polynomial

nore that when x = 0 y = 0 so it passes through the origin

Answer 9

oh so the question is asking over what axis is the graph symetrical? what would be an example of a graph being symetrical on the origin? sorry i just have a hard time understanding what questions are asking

Answer 10

would an ellipse be symetrical on the origin?

Answer 11

Sorry I lost the web

x^2 + y^2 = 4
is a circle symmetrical about the origin

Yes an ellipse could be symmetrical about the origin also

Answer 12

No sorry - an ellipse might be symmetrical about the x or y axis,

Answer 13

2) try solving -5x^2 + 4x = 0 to find where it cuts the x-axis

Answer 14

* -5x^2 + 4x = 0

Answer 15

gotta go - I forgot my soccer team are playing portugal in semifinal!

Answer 16

sorry i went to watch it too lol. good luck! Wales is playing resally good, its gonna be a nice game