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.
