0:02 so ladies and gentlemen so far what we
0:05 have um basically discussed is going to
0:08 be uh quad our linear equations all
0:10 right now what we're going to be doing
0:11 is with quadratics and the reason that
0:14 we um get into this would be a quadratic
0:16 is going to be based
0:18 on that little two there which is going
0:21 to be our degree okay so for this whole
0:22 chapter chapter four we're going to be
0:24 dealing with quadratics that means
0:26 you're going to have an equation or we
0:28 might be dealing with functions that
0:29 we're going to have your variable is
0:32 going to be to the second power okay
0:33 sometimes we'll have a linear variable
0:35 as well but you're always going to have
0:37 for quadratics for it to be a quadratic
0:39 and you have to have a variable raised
0:42 to the second power okay so what we're
0:43 going to learn how to do is graph these
0:47 now when we're learning how to uh graph
0:48 linear equations you know there's kind
0:50 of two different things that I you know
0:51 told you if you had a linear equation y
0:57 = 3x - 1 right um we talked about you
0:58 can always use like a table values you
1:07 right yes right do you
1:10 remember that you can take X and then
1:12 plug in y and then plot the points
1:13 connect them but that but the reason
1:15 with that is that was a lot of work
1:17 right so what we also found out was we
1:19 could also use slope intercept
1:23 form right and just find what m is find
1:26 what B is plot the point negative 1 and
1:29 then use that as your slope 1 2 3 over one
1:30 one
1:31 and then you could
1:34 connect right it was pretty simple does
1:36 everybody understand kind of with me
1:39 okay so um or we or if it was in
1:40 standard form we use the intercept
1:43 method now for a
1:46 quadratic um the shape
1:48 shape
1:52 yes yes that that was just a that wasn't
1:53 really a part of this problem I'm going
1:54 to get into that that was just a little
1:58 forward um and we what you're doing
2:01 sorry so into graphing quadratics what
2:02 we're going to be doing is we're going
2:05 to use the first method okay which is
2:07 when you have a quadratic in standard form
2:08 form
2:11 now a quadratic the shape of the
2:13 quadratic is not like a line it is what
2:15 we call a
2:18 parabola and a lot of
2:23 times you can just relate it to a
2:27 u okay so the reason why I show you guys
2:29 this what you know some examples of a
2:32 prev look like though are because if you
2:35 just pick two points does that tell you
2:38 what the graph looks like no it doesn't
2:41 right hey gu girls this
2:43 is this is what I'm going over this is
2:45 the important thing I know this is the
2:47 important things right here so picking
2:49 two points is not going to be enough all
2:51 right and there's another thing I want
2:52 you guys to understand I want you to
2:53 make sure you write down when we're
2:55 dealing with quadratics there's a very
2:57 very important Point there's actually
3:00 two there's a two kind kind of important
3:03 characteristics the minimum or the
3:05 maximum and whenever you have the
3:09 Min or the maximum point do you guys see
3:10 how that's like the minimum point of
3:12 this Parabola right here and that's the
3:14 maximum Point any point that it takes
3:16 the minimum or the maximum is what we
3:27 vertex okay so you're going to want to
3:29 make sure you understand that the next
3:32 thing is through the vertex there is a
3:34 line of
3:37 symmetry so I'm not going to be the best
3:39 drawer here but if you guys remember in
3:42 Geometry a line of symmetry is a line
3:44 about where which you can flip your
3:45 graph over and it's going to be
3:46 symmetrical with do you guys see that if
3:48 you were to kind of take that and fold
3:51 it over that dotted line okay right
3:54 Elizabeth from geometry right right no
3:56 I'm just saying from remembering from geometry
4:03 okay does everybody see what we have
4:08 here yes okay so when we're getting into
4:10 graphing now what we're going to do when
4:12 we're graphing in a when we graph a
4:14 quadratic what I'm going to expect you
4:16 guys to do is the first thing we're
4:17 going to do is find the vertex we're
4:19 going to find that point and we're going
4:21 to plot that point remember when we
4:22 graph linear equations the first thing
4:25 we did was graph the Y intercept right
4:26 now the first thing we're going to do is
4:29 graph the vertex okay then what we're
4:32 going to do is pick two
4:35 points to graph either to the left or to
4:37 the right of the vertex and once you
4:38 know two
4:41 points can you now use those other two
4:43 points or the line of symmetry to
4:45 reflect over there so really ladies and
4:46 gent all we're going to do is now
4:47 instead of two points we're now going to
4:49 up ant it up to three points that we're
4:51 going to graph and then you're just
4:53 going to reflect those other two points
4:55 across the line of symmetry and then you
4:57 have five points that you can use to
5:03 well let's go and see what we're going
5:14 vertex so the vertex the formula for the
5:19 vertex equals opposite of B / 2
5:22 a and some of you might say okay where
5:25 did you get the a and the B well if you guys
5:27 guys
5:31 remember ax plus b y yal C that was what
5:33 we wrote for that was standard form of a
5:36 linear equation right so standard form
5:46 this do you guys see that that is your
5:47 standard form for your equation so now
5:49 all I got to
5:51 do um actually kind of my steps that I
5:53 like to do is first thing identify my a
5:59 b and my C A = 1 B = 8 C = 12 does
6:03 everybody see how I labeled my a b and c
6:07 yes okay now I'm just going to evaluate
6:10 to find my vertex so I do opposite of 8
6:12 / 2 *
6:22 -4 Everybody follow
6:26 me so now I don't know my vertex though
6:28 I don't know what that point is all I
6:30 know is that
6:31 that
6:40 shoot I'm sorry that's not the vertex
6:50 symmetry sorry if you guys remember when
6:52 I did this
6:55 graph remember here was the vertex
6:58 right remember the axis of symmetry goes
7:01 through the vertex X right notice that's
7:03 a vertical line vertical lines are in
7:05 the form of x equals correct so I'm
7:08 sorry I just been over break I I Mis
7:11 stoed my thing so Elizabeth when I'm
7:14 describing this your ver your horizontal
7:15 line is your vertex so the first thing
7:17 we want to do is not find the vertex but
7:19 we want to find the axis of symmetry
7:22 which is the x coordinate of my vertex
7:30 a I do opposite of B divid by 2 a and I
7:35 get X4 therefore I go an X4 1 2 3 4 and
7:57 that axis symmetry always equals xals
8:00 opposite of B / 2 a
8:01 yes you're going to want to have that
8:02 memorized because you are going to have
8:08 that um my apologies I it's been a long
8:10 break but does everybody see that and understand
8:13 understand
8:16 itos okay now where is this point though
8:18 lie on this graph well to do that you're
8:21 going to have to go back to your table
8:29 so X Y we know that our coordinate is
8:33 4 right so to find the y coordinate we
8:38 got to plug -4 in for X so I do y = -4
8:44 2ar + 8 * -4 + 12 does everybody see
8:46 what I did there I took my x coordinate
8:47 and I plugged it into my equation to
8:53 find my y-coordinate and I get y = 16 -
9:09 -64 right so now I go left4 and now I go
9:12 down4 1 2 3
9:19 vertex what's
9:22 necessary all you've done is do opposite
9:25 of b divid 2 a you found that value and
9:27 then you plug it back into the equation
9:30 okay now let's pick we need to pick two
9:31 more points as I mentioned we need to
9:32 pick two points to the left or two
9:34 points to the
9:36 right what would you like to do pick two
9:38 points to the left or to the
9:41 right to the left
9:44 like well my recommendation would always
9:46 be smaller numbers right it's much
9:48 easier to pick numbers that are smaller
9:51 than going larger I mean larger in like
9:54 absolute value right so let's just do to the
9:56 the
10:13 when doing that I get y = 9 - 24 + 12
10:17 that becomes uh -12 9 that becomes
10:20 -3 so that becomes
10:41 and when I get to that um I get zero
10:59 right okay so what the main important
11:00 thing that I want you guys to see now is
11:03 I've graphed one part of my Parabola
11:05 I've graphed the right side of this but
11:07 remember these are symmetrical to get to
11:10 this point I went over one over over one up
11:15 one to get to this point oh shoot I'm
11:18 sorry it's right there I went over two up
11:24 four right I'm sorry my graph is all wrong
11:26 wrong
11:29 here so now to get to my next point I'm
11:31 going to go over one up one to get this
11:33 next point I'm going to go over two up to
11:43 there anybody have any questions on
11:46 this anybody have any questions
