00:03
Okay, so the first part of this question is a little difficult because i don't have the actual graph, but i can talk through what you should be looking for with this question so you can try and manipulate it.
00:15
But it says that between 1990 and 2013, there's a drop a violent crime and a spike in the prison population in the united states.
00:22
And there's two graphs.
00:23
And in those graphs, i'm going to have to imagine that something along these lines happens that the violent crimes, probably not exactly like this, dips down.
00:34
The number of people in the prison is going up.
00:38
So something along those lines.
00:41
And again, i'm assuming some things that these are on the same graph and not a different graph.
00:45
So there's some liberties i'm taking here, but you kind of get the idea.
00:49
We're looking for where that point of intersection probably is and what years is going to be in between.
00:54
So your graph shouldn't look something along these lines, maybe two of them.
00:58
And just knowing, okay, these two points appear to be between between 1998 and 1999, or 2003 and 2004.
01:07
That is for you to look at when you are looking at the graph.
01:11
And the second part gives us a couple of equations that the information is modeled off of.
01:19
So our violent crime equation is y equals 0 .6x squared minus 28x plus 730.
01:36
The prison population equation is negative 15x plus y equals 300.
01:46
And we have to figure out what x and y are for these two equations.
01:50
And we couldn't if we'd only have one equation.
01:52
Thankfully, we have two.
01:54
So what we're going to do first is manipulate the equation that deals with the prison population so that y is all by itself.
02:04
So i'm going to add 15x to both sides.
02:06
And that's the opposite of the minus the negative 15x.
02:10
I get y equals 15x plus 300.
02:15
You write 300 plus 15x? yes.
02:18
But i like to put my stuff in order from highest exponent to lowest exponent, and there is no variable or exponent of 300, so i guess to do last.
02:29
Now, in order to figure out everything else, we're going to start with setting these two equations equal to each other and solving for x.
02:36
Because we know the ys have to be the same thing.
02:39
It's shown there, y equals this and y equals this.
02:43
So we're going to substitute one into the other one.
02:47
So 0 .6x squared minus 28x plus 730 is equal to 15x plus 300.
02:59
Now we're going to take these two pieces, the negative 15x and the negative positive 300, or sorry, positive 300, and we're going to subtract them over.
03:10
So we're going to subtract 15x here.
03:11
So i'm lining up with the terms that are the same.
03:18
And i'm jumping a little bit with these combinations.
03:22
But when we do, we still have that 0 .6x squared, minus 28x, minus 15x is minus 43x, plus 730, minus 300 is plus 430.
03:37
And then these pieces over here, both cancel outs for left with equals to zero.
03:44
Now, our next job is figure out what the heck x is, and this is a quadratic, so we can use the quadratic formula.
03:52
And the quadratic formula is, you know, i grace my graph over here, because we're all done with that, give myself a little bit of space.
04:09
So i can write out that formula and then fill it in and work out all the math.
04:16
Just like almost all colored out there...
