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

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Answer 1 · 2016-12-23T14:53:23

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

$y=x^2+x+1$

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.

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