Question #f986a

1 Answer
Oct 4, 2017

#y=x^2#:
graph{x^2 [-40, 40, -20, 20]}

#-6+y=x#
graph{x+6 [-80, 80, -40, 40]}

Explanation:

Let's graph these one by one.

#y=x^2# is your standard form of a parabola, and a pretty common shape.

You can graph this by subbing in points:
when #x=1, y=(1)^2=1#
when #x=2, y=(2)^2= 4#
when #x=3, y=(3)^2=9# and so on.

Or, you can memorise what this graph looks like. It has a vertex at the origin, with two arms branching upwards on either side of the y-axis:
graph{x^2 [-40, 40, -20, 20]}

#-6+y=x# is a different type of graph. By looking at it, you can tell it is line (i.e. a straight line) as its highest power of #x# is 1.

(Note: #1x# is the same as #x#.)

To graph this one, you need to find the x- and y-intercepts:

x-intercept (when y=0):
#-6+0=x#
#x=-6#

So the graph cuts the x-axis at #-6#.

y-intercept (when x=0):
#-6+y=0#
#y=6#

So the graph cuts the y-axis at #6#.

You then plot these two points on a graph and draw a straight line that goes through both points:

graph{x+6 [-80, 80, -40, 40]}