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NationalTutoringObservatory
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MathEd-PII

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8
volunteer
Yeah, basically
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volunteer
and like, you know how the quadratics and like X^2 point the same direction?
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student
Mhm
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volunteer
Yes.
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volunteer
All right, we can move on now.
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student
Well, can I read this, the leading coefficient is negative.
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student
when and behavior is, what did I mean write down, look up.
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student
Oh. Yeah, yeah.
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volunteer
You notice how the right side is pointing down, and on this side pointing out, yes.
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volunteer
That's why
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volunteer
Uh-huh.
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student
Wait, can I, can I say one more question on this just to make sure I got it.
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volunteer
This would be uh, this would be a, um, even one though.
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student
So negative. So, I mean, odd.
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student
since it's both like.
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volunteer
So, well, first of all, let's find the degree.
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student
OK
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volunteer
So how many times does it cross the X-axis.
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student
Um
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volunteer
OK, I have noticed a new thing, so I'm just gonna tell you this now. You see how it's going into
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volunteer
a
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volunteer
X value at a curve.
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student
right here
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volunteer
Yes, that would mean that that's cubed, the multiplicity would be 3.
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student
Oh.
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volunteer
You see how it's going into that like swooping motion.
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student
Mhm
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volunteer
Yes, that would mean that the X value.
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volunteer
to the power of 3
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volunteer
So take that into account when you're counting the times it crosses the x-axis.
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volunteer
So that
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student
Oh, OK. So when
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volunteer
mhm
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student
2
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volunteer
Good
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student
3
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volunteer
Yup
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student
6
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volunteer
Yes
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student
so even
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volunteer
Yup
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student
The leading coefficient, uh, negative.
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volunteer
Good. And do you know why it's negative?
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student
cause they're facing now
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volunteer
Good
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student
and there are different zeros.
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volunteer
Yup, because there's a multiplicity of 3
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volunteer
on this
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student
and to maximums.
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volunteer
Is there 2? Yep.
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volunteer
Good job. See, you do it.
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student
Was, OK. OK, I got it. OK, so, OK.
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student
So I'm, I'm trying to write this down.
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volunteer
No problem. Take your time.
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student
OK
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volunteer
All right. So, plot the X intercepts and make a signed chart that represents the functions shown below. All right, so you see it's negative, X + 2 x minus 1.
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volunteer
and x minus 6
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student
a negative X minus 2.
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volunteer
So what would that be
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student
Would that be equals 2.
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volunteer
I think so
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student
or
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volunteer
I've never seen it written like that, but that seems correct.
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student
or X equals -2.
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volunteer
Right, negative X
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volunteer
minus 2
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volunteer
Yes, so the X would equal 2.
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student
OK, so
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student
hold on
16,453
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student
Well, it'll be negative too, negative X minus 2.
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volunteer
Yeah, well, yeah, if you distribute the negative, it would be negative X minus 2, which would just be 2, right?
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student
X minus 2
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volunteer
Yep.
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student
Oh, I thought it would be, um, I thought it would be.
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volunteer
Well, well, what would negative X minus 2? How would negative X minus 2 equals 0.
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student
1 X is.
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student
2
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student
Oh wait, no
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volunteer
Yes
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student
So it was you
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volunteer
Look, because X
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volunteer
minus 2
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volunteer
-x - 2 = 0
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volunteer
equals 0, right
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student
Yeah
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volunteer
And so, if X is equal to -2
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volunteer
that would just be
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student
Mm.
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volunteer
2 minus 2 equals 0. So yeah, you would just basically ignore that negative because it's not attached to an X or anything.
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student
So
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volunteer
and you just focus on the functions.
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student
this will be X
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student
equals 1
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volunteer
Yup
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student
Wouldn't this be 2 times, so.
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student
yeah
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volunteer
It would be a multiplicity, but I'm pretty sure if it's a number chart, you would just do it once.
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volunteer
And now we do a sign chart
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student
uh.
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volunteer
So do you know how to do this?
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