Question

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

Answer 1

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 `(x+2)^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=(-2+2)^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.
`(x+2)^2=0`
`x+2=+-sqrt0`
`x=-2+-sqrt0`
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=(0+2)^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`