How do you find the intercepts, vertex and graph #f(x)=x^2-4x-5#?
You can use the quadratic formula, the "zero" function on a graphing calculator, factoring, or completing the square to find the solutions. This function is very straightforward to factor. If you're not comfortable with factoring, you can learn about it and practice on Khan Academy. He calls it "factorization": https://www.khanacademy.org/math/algebra/polynomial-factorization.
Finding the vertex is more complex. I like to use the first few steps of completing the square to change the function from "standard form" into "vertex form".
Dr. Khan covers this too, if you're not comfortable with it yet: https://www.khanacademy.org/math/algebra/quadratics/quad-standard-form-alg1/v/ex3-completing-the-square.
Putting this in vertex form yields an equation of the form