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

1 Answer
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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 #(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#

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