Question

How do I find the vertex, axis of symmetry, y-intercept, x-intercept, domain and range of `y=-x^2+4x+1`?

Answer 1

The method used is completing the square.

Explanation:

So first let's find the line of symmetry and the vertex.

To complete the square..

-x^2+4x+1=0
-x^2+4x+2^2+1-2^2=0
y=(-x+2)^2-5
-x=2, hence x=-2. and y=-5.

Domain is the set of x values, probably the most confusing concept I've come across in maths till now, yes, I'm ashamed of it.
Although, with the square completed now..

(-x+2)^2=y+5
y+5>0
y>-5
With the range found, plotting a graph and using at least 4 suitable values would help to find the domain.