# How do you graph f(x) = (x + 2)^2?

Apr 10, 2018

graph{(x+2)^2 [-10, 10, -5, 5]} This is the actual graph, for a sketch graph read the explanation

#### Explanation:

f(x) is just another way of writing y, by the way

First, find the vertex.
To find the x coordinate, set ${\left(x + 2\right)}^{2}$ to equal 0. To get an answer of 0, x must equal -2.
Now, find the y coordinate by substituting -2 in for x.
$y = {\left(- 2 + 2\right)}^{2} = 0$
The vertex is (-2,0). Plot this point on the graph.

To find the roots (or x-intercepts), set y equal to 0 and solve the equation to find both values of x.
${\left(x + 2\right)}^{2} = 0$
$x + 2 = \pm \sqrt{0}$
$x = - 2 \pm \sqrt{0}$
As we can see, the graph has a repeated root at (-2,0). (Coincidentally, this is the same as the vertex). Plot this point.

Now, find the y-intercept by substituting 0 for the value of x in the equation. $y = {\left(0 + 2\right)}^{2} = 4$. The y-intercept is (0,4). Plot this point,

Now, draw a smooth symmetrical curve joining the plotted points, with the line of symmetry being the line $x = - 2$