Graphing Quadratic Equations - Free Educational videos for Students in K-12

Graphing Quadratic Equations - By Marc Whitaker

Transcript


00:03	graphing quadratic equations . Here we have a quadratic equation
00:08	. X squared plus six X plus five equals y
00:13	after . Remember that ? That's one . So we
00:18	have to figure out what the coefficients are . A
00:20	equals one b equals six c equals bye . Now
00:32	we can use the front end of the quadratic formula
00:38	to find the line of symmetry , which is the
00:41	first half of the Vertex . So X equals negative
00:46	B over two A . In this case , that's
00:52	negative . Six over two times one which is negative
00:58	. Three . So X equals negative . Three is
01:04	the line of cemetery and it's half the Vertex .
01:08	So the line of symmetry would be over here somewhere
01:15	. Now we're going to find a few points to
01:19	plot X . Why , we're gonna start with the
01:27	Vertex or a line of symmetry and put that in
01:34	the middle . So we know the equation is X
01:40	squared plus six times X plus five . That's ex
01:51	. That's X , which is going to be negative
01:53	. Three Negative three squared is nine six times negative
01:58	. Three is negative . 18 plus five nine plus
02:04	negative . 18 is negative . Nine Negative nine plus
02:07	five is negative , for we're going to pick a
02:14	few other points . Negative four . Negative five Negative
02:19	. Two . Negative one . Since this shape is
02:25	symmetric , we know that these two pairs those answers
02:34	will be the same . And for these two pairs
02:38	, those two answers will be the same . Which
02:41	cuts our work in half . We only have to
02:43	find one of them , and then the other one
02:45	comes along for free and the principle that smaller numbers
02:49	are easier to work with . I'm going to do
02:51	these two , and then these two answers will come
02:53	along for free . So this is X squared plus
02:57	six X plus five . So that's negative . Two
03:03	. Squared negative . Two . So that's four plus
03:09	negative . 12 is negative . Eight . Negative eight
03:14	plus five is negative . Three . Negative three and
03:22	negative one negative one squared plus six times negative .
03:26	One plus five one plus negative six is negative .
03:31	Five plus five is zero , and that's going to
03:36	be zero . Zoom in on this for a second
03:41	, so you can see what I did . Alright
03:46	, now it's time to graph these things . Negative
03:54	. Five zero It's negative . Five zero Negative four
04:01	Negative three Negative 1234 Negative 12 three Negative three negative
04:08	. Four negative . 123 We have 123 four .
04:14	So that's enough for me to sketch at first graph
04:24	. If we continue , I'm going to bet that
04:26	this side's got to look pretty much the same because
04:29	it's symmetric . So negative , too negative . Three
04:33	Negative two negative . Three . Negative 10 Negative one
04:40	zero and it is . And we sketch the graph
04:47	of the quadratic equation . Notice that the Vertex is
04:53	that negative . Three . Negative four And the Vertex
05:01	was the first point we found . We're going to
05:08	do another one in just a moment . All right
05:11	, Here's our second example , and once again ,
05:14	the coefficient of the square term is one . So
05:18	we have a equals one b equals six c equals
05:24	nine . So when it's time to find the Vertex
05:28	, we start by finding the line of symmetry ,
05:31	which is half the vertex . That's X equals negative
05:36	B over two A . In this case , that's
05:41	negative . Six over two times , one , which
05:49	is negative . Three . So once again , the
05:53	line of symmetry happens to be at at negative three
05:57	. Not that it's always at negative . Three .
05:59	Just is on the two examples I happen to have
06:01	picked , so ax equals negative three . Now we
06:07	need to yes , find some more points . 12345
06:21	six points . We're going to start with negative three
06:28	negative two negative 10 negative . Four . Negative five
06:36	. And if you remember the equation , it's X
06:42	squared . Plus six x six plus nine when X
06:52	is negative . Three . Negative three squared is nine
07:01	plus negative . 18 is negative . Nine plus nine
07:05	is zero negative . Two . It's negative . Two
07:14	squared plus six times negative . Two plus nine .
07:24	That gives us four plus negative . 12 is negative
07:29	. Eight . Negative . Eight plus nine is one
07:33	, and that's going to be one . Because I
07:35	know those two have to match . So next I'm
07:42	going to do one negative one . I'm sorry .
07:45	Negative . One squared , plus six times negative .
07:47	One plus nine . One plus negative . Six is
07:53	negative . Five negative . Five plus nine is four
07:59	. And I know those to match . So this
08:04	is four . And I'm gonna add one more point
08:07	. I'm gonna do zero because it's so easy .
08:09	Zero squared , plus six times zero plus nine .
08:16	So zero plus zero plus nine is nine . Now
08:23	that I've got some points , let's see if I
08:29	can graph these and see what it looks like .
08:32	Negative . Five four Negative . 123451234 Negative . Four
08:43	. One Negative . Three zero Negative . Two one
08:54	. Something's wrong here . What did I do wrong
08:57	? One . No negative 14 That's not wrong .
09:02	Negative . One four and zero , nine 1234567 eight
09:14	nine Would be somewhere up there as an estimate .
09:20	So hopes . That's not very neat . Job looks
09:28	roughly like that . If you have questions , don't
09:35	hesitate to come in and ask me .

Summarizer

DESCRIPTION:

Instructor uses a white board to model graphing quadratic equations. Examples show using quadratic equations in standard form to determine the line of symmetry, create a table of values, and graph the quadratic equation by using these values.

OVERVIEW:

Graphing Quadratic Equations is a free educational video by Marc Whitaker.It helps students in grades 9,10,11,12 practice the following standards HSF.IF.C.7.a.

This page not only allows students and teachers view Graphing Quadratic Equations but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.

1. HSF.IF.C.7.a : Graph linear and quadratic functions and show intercepts, maxima, and minima.