# How do you graph y=x^2+4x+6?

Aug 8, 2015

Graph $y = {x}^{2} + 4 x + 6$

#### Explanation:

To graph a parabola, fins a few critical points, such as: vertex, axis of symmetry, y intercept and x-intercepts.
x-coordinate of vertex: $x = - \frac{4}{2} = - 2$
(y-coordinate of vertex: y = f(-2) = 4 - 8 + 6 = 2
Axis of symmetry: x = -2
y-intercept --> Make x = 0 --> y = 6
x-intercepts --> Solve y = 0.
D = 16 - 24 = - 8 < 0.
There are no x-intercepts. The parabola is completely above the x-axis.
Since a> 0, the parabola opens upward, there is a min at vertex.
graph{x^2 + 4x + 6 [-10, 10, -5, 5]}