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

Dec 23, 2016

Vertex at $\left(- \frac{1}{2} , \frac{3}{4}\right)$
Y intercept at $\left(0 , 1\right)$
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 $y = a \left(x - h\right) + k$
$y = {\left(x + \frac{1}{2}\right)}^{2} + \frac{3}{4}$

Intercepts:
The y intercept is at $\left(0 , 1\right)$. 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.