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

Nov 1, 2015

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

#### Explanation:

To find the x-intercepts, set y = 0
so ${x}^{2} + 2 x + 1 = 0$
Factorise this to $\left(x + 1\right) \left(x + 1\right) = 0$
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]}