Question

What are the important points needed to graph `f(x)= -x^2+2x+1`?

Answer 1

You need the x and y intercepts and the vertex of the graph

Explanation:

To find the x-intercepts, set y = 0
so `x^2 + 2x + 1 = 0`
Factorise this to `(x + 1) (x + 1) = 0`
So there is only one x-intercept at x = -1; that means the graph touches the x-axis at -1

To find the y intercept set, x = 0
So y = 1

This means that the graph crosses the y-axis at y = 1

Because the graph touches the x-axis at x = -1 then that is the
x co-ordinate of the vertex and the y co-ordinate is y = 0 and it looks like this graph{x^2 +2x +1 [-5, 5, -5, 5]}