Question

How do you identify the important parts of `y = x^2 + x + 1` to graph it?

Answer 1

Vertex at `(-1/2,3/4)`
Y intercept at `(0,1)`
No x intercepts graph{x^2+x+1 [-10, 10, -5, 5]}

Explanation:

`y=x^2+x+1`

Vertex:
Complete the square into vertex form `y=a(x-h)+k`
`y=(x+1/2)^2+3/4`

Intercepts:
The y intercept is at `(0,1)`. We know this because if we plug in 0 in for x, the output is 1.

There are no x intercepts because the parabola is facing up and has a vertex above the x axis.