Precalculus, Intercepts and Symmetry

Question

I really need help in finding the x and y intercepts for the following graphing equation: 2x=3y^2. I know how to test for symmetry but this question confused me. Please help me!!!!!

Answer 1

The x-intercept is the point of intersection of the graph to the x-axis, (x,0). So to determine the x-int. plug in 0 for y, y=0, then solve for x.

 

And to determine the y-intercept plug in 0 for x, x=0, and solve for y, since y-int. is the point of intersection of the graph to the y-axis.

 

If you look at the equation you will notice that it is a parabola that opens to the right with the vertex at the origin. Therefore, the best way to determine the intercepts is to recognize the nature of the equation.

 

The line of symmetry therefore is the x-axis.