We're asked to graph y is equal to x squared minus x,
minus 6 by plotting points.
Let's just make a table.
Let's just pick some x values, and figure out what y is going
to be based on this relation up here.
So let's figure out what y is going to be.
So let's just start x at negative 3.
So if x is negative 3, then y is going to be negative 3
squared is 9, minus negative 3-- so that's
plus 3-- minus 6.
So what is that?
9 plus 3 is 12, minus 6, this is equal to 6.
Then we get-- let's just keep going before we plot any
points-- so then we have negative 2.
If x is equal to negative 2, then y is negative 2 squared,
which is 4, minus negative 2, so that's plus 2, minus 6.
So in that situation, we have 4 plus 2, minus 6,
it's equal to 0.
Then if x is equal to negative 1, we have negative 1 squared,
which is positive 1, minus negative 1, which is another
positive 1.
Then we have minus 6.
2 minus 6 is equal to negative 4.
Let's go to 0.
If x is equal to 0, these two terms are 0.
And then y is equal to negative 6.
So let's just go all the way to positive 3.
If x is equal to 1, we have 1 squared minus 1.
Those cancel out.
And then you have just a negative 6 there.
And then if we have x is equal to 2, we have 2 squared, which
is 4, minus 2, minus 6.
So 4 minus 2 is 2, minus 6 is equal to negative 4.
And then if x is equal to 3, we have 3 squared, which is 9,
minus 3, right?
9 minus 3, minus 6.
Well that's going to be equal to 0.
So let's plot these points.
So let me do it in a dark color here.
So the first point is negative 3 comma 6.
So this is my x-axis right here, this is my y-axis.
So negative 3 is negative 1, 2, 3 comma 6.
1, 2, 3, 4, 5, 6.
So it will be right over there.
That's this point over here.
And the next 1 is negative 2 comma 0.
So negative 2, and then we don't move up in the y
direction at all.
Then we have a negative 1 comma negative 4.
Negative 1.
1, 2, 3, 4.
Negative 4 is right over there.
Then we have 0, negative 6.
0, x is 0.
y is negative 6.
So it's that point right there.
Then we have 1, negative 6.
So x is 1, y is negative 6.
And then we have-- and then what do we have?
We have 2, negative 4.
So x is 2, y is negative 4.
And x is 3, y is 0.
So you can see, here, if we just connect these plots, we
get a bit of a curve.
We get a bit of a u shape.
And the u shape will look like this.
I'll do my best to draw it, this is always the hardest
part, connecting the dots.
So let me just do it in one nice-- so you get a u shape
that looks something like that.
I can do a better job of drawing that, I'm sure.
Let me do one last shot at this.
So let me just draw as good of a u shape as possible, just
keep going like that.
So you get this u shape over here.
And this u shape, which is the general shape of these
quadratic functions right here,
this is called a parabola.
So that u shape is called a parabola.
And in the future we'll see better ways to graph it, so
you don't have to just plot a bunch of points.
But it's good to see the general shape, and we get that
general shape just by trying out a bunch of x values and
figuring out the corresponding y values.