Question

Hi! How do you sketch y^2=x^3+9x

Answer 1

Assuming its not a circle or a hyperbola (I don't know the formulas for both, but I know they involve y^2), we square root to get:\[y=\sqrt{x^3+9x}\]\[y=\sqrt{x(x^2+9)}\]
Since you cannot take the square root of -9, the only root is 0.
Since you cannot take the square root of a negative number, we know that everything below 0 CANNOT exist (0 does b/e sqrt(0) = 0).
Since the power in the radical is higher than the radical itself, the ending would look like a cubic function: