I was wondering how to find the x and the y intercepts of the following equation

y = xe^(-x^2/2)

I know for a fact that the intercept is through 0,0 but I don't know how to do this long hand.

When x is zero, y is zero, and vice versa.

To find the x-intercept (where the graph crosses the x-axis) of the equation y = xe^(-x^2/2), we set y to zero and solve for x.

Let's set y = 0 and solve for x:

0 = xe^(-x^2/2)

Since anything raised to the power of 0 is 1, we can divide both sides of the equation by e^(-x^2/2):

0 = x

So the x-intercept is x = 0. This verifies what you mentioned, that the intercept is through (0,0).

To find the y-intercept (where the graph crosses the y-axis), we set x to zero and calculate the corresponding value of y.

Let's set x = 0:

y = 0*e^(0) = 0

Therefore, the y-intercept is y = 0.

In conclusion, the intercepts of the equation y = xe^(-x^2/2) are x = 0 and y = 0.