Question

Question #f986a

Answer 1

`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]}