ShmoopTube

00:00

Thank you We sneak in and here's your smoke du

00:05

jour Brought to you by parabolas They have an appointment

00:08

scheduled with a plastic surgeon so they can do something

00:11

about their drooping graph Below shows the roots of a

00:14

parabola given that the parabolas equation has an x squared

00:17

term with the coefficient of one select the vertex of

00:20

the para boola by clicking the appropriate region of the

00:23

graph let's See if we can figure out what's going

00:26

on here We've got a graph with two points this

00:29

little guy here and little buddy over here and we're

00:32

told that they're the roots of a parabola Our mission

00:35

way choose to accept it We better passes Test is

00:38

to locate the vertex of the rabble of well The

00:42

problem makes a big deal out of the fact that

00:43

the x squared term has a coefficient of one So

00:46

that has to be important somehow First of all the

00:48

fact that the coefficient is positive tells us that the

00:51

parabola has to open the ports meaning the vertex has

00:55

to be below the routes We also know that the

00:57

vertex like any vertex will be the same distance from

01:00

one root as it is from the other we just

01:03

don't know how low it can go How do we

01:05

figure that part out Well we use our handy dandy

01:08

parabola equation which any time r x squared coefficient is

01:12

one is why equals x minus the first ruth times

01:16

x minus the second route Well the roots according to

01:19

the graph our negative two and four of the equation

01:21

and have to be Why equals Acts minus negative 2

01:25

times acts minus four or canceling the negative signs get

01:28

x plus two times x minus four Now if we

01:32

just plug in x equals one to get the matching

01:35

why co ordinate we get why equals one plus two

01:38

which is three times one minus four is all negative

01:42

three and three times thinking of three at least in

01:44

california is negative Nine door x is one and our

01:47

wise negative nine which means our vertex will be at

01:50

point one Negative nine that's about as droopy is droopy

Full Transcript