How to graph a parabola #y = (x + 2)^2 + 2#?

Question

Eva Adamson · Accepted Answer

#y = (x+2)^2+2#

The vertex of this parabola will be where #(x+2) = 0#, that is where #x = -2# and #y = 0+2 = 2#, that is at #(-2, 2)#.

The axis is vertical, given by the equation #x = -2#.

The intercept with the #y# axis will be where #x=0#, so

#y = (0+2)^2+2 = 4+2 = 6# - that is at #(0, 6)#

#y->oo# as #x->+-oo#

If you want any more points, just substitute them into the equation of the parabola.

graph{(x+2)^2+2 [-11.87, 8.13, -1.68, 8.32]}

Abigail Allen · Answer

undefined To graph the parabola y = (x + 2)^2 + 2, you can follow these steps:

1. Identify the vertex of the parabola, which is (-2, 2).
2. Since the coefficient of x^2 is positive, the parabola opens upwards.
3. Plot the vertex (-2, 2) on the coordinate plane.
4. Use the symmetry of the parabola to plot another point equidistant from the vertex on the other side of the axis of symmetry.
5. Plot additional points by choosing x-values and substituting them into the equation to find the corresponding y-values.
6. Draw a smooth curve through the plotted points to represent the parabola.