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 . |

#### 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.

GRADES:

**9101112**

STANDARDS:

**HSF.IF.C.7.a**