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

##### 1 Answer

Oct 10, 2015

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.