how do I find the x and y intercepts for the graph of y=x^2+4x-17

The y intercept occurs where x = 0.....this is at (0, -17)

Here's a graph of the x intercepts.....

https://www.desmos.com/calculator/mw8haweyzs

They occur at about x =- 6.583 and at  about x = 2.583