How do you find the vertex and intercepts for #y² - 4y - 8x +25 = 0#?
First reorder to get one of the variables (in this case x) on its own.
Then use completing the squares to get the expression into the form
The vertex occurs where the bracketed term is zero and is therefore
The x intercept occurs where
The y intercepts occur where
This shows that there are no real roots to the equation, only imaginary ones.