Question

What are the important points needed to graph `y=x^2+2x+1`?

Answer 1

Graph `f(x) = x^2 + 2x + 1.`

Explanation:

The important points are:
1. x-coordinate of axis of symmetry.
x = -(b/2a) = -2/2 = -1.
2. x-coordinate of vertex: x = -(b/2a) = -1
y-coordinate of vertex:
f(-1) = 1 - 2 + 1 = 0
3. y intercept.
Make x = 0 --> y = 1
4. x-intercepts.
Make y = 0 and solve `f(x) = x^2 + 2x + 1 = (x + 1)^2 = 0`
There is double root at x = -1.
graph{x^2 + 2x + 1 [-10, 10, -5, 5]}