Question

Create a quadratic equation and demonstrate how it would be solved by graphing, factoring, the quadratic formula, and by completing the square.

Answer 1

Well can you create one for us?

Answer 2

First off do you know what a quadratic equation looks like?

Answer 3

I wouldn't know where to start...

Answer 4

not right off the bat but I have been studying it.

Answer 5

can you help me on the first to , I have an Idea on squaring but the other two not really.

Answer 6

\[ax^2 + bx + c = 0\]

Answer 7

okay.

Answer 8

That's how a general quadratic equation looks like. Where a b and c are any values

Answer 9

a usually equals 1 to make it easier to solve

Answer 10

so I just have to fill thos in with #'s??

Answer 11

Well like I said a is 1 to make it easier to solve.

Then b and c have some connection to each other in order to use the complete square method

Answer 12

so like 2 and 4?

Answer 13

Well it's more complicated than that

Answer 14

For example
(x + 2) ( x+2)

Answer 15

give you x^2 + 2x + 2x + 4= x^2 +4x+4

Answer 16

yah, but that's after factoring right?

Answer 17

in this case b=4 and c=4

Answer 18

Yeah

Answer 19

oh okay.

Answer 20

But I'm talking about completing the square.

Answer 21

yah, I got the hang of it now. But what about the quadratic factoring.

Answer 22

It's hard for me to explain that part but try other example like

(x+2)(x+1)

Answer 23

To see what b and c equal

Answer 24

uh-huh.

Answer 25

(x+2)(x+1)= x^2 + 2x + x + 2= x^2 + 3x + 2

Answer 26

in that case b=3 and c=2

Answer 27

are we still talking about completing the square?

Answer 28

yeah

Answer 29

okay.

Answer 30

Lets say a=1 b=4 c=4 what's the general equation look like?

Answer 31

it's going to be this equation ax^2 + bx + c = 0? or is this for somthing else?

Answer 32

Yeah exactly like that

Answer 33

so all these examples that you just did can be pluged in for that?

Answer 34

and that's jusr for completing the aquare or general form now?

Answer 35

No you can solve using quadratic formula for example

\[\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array} \]

Answer 36

You plug in a b and c to the left and solve for x

Answer 37

ah, okay.

Answer 38

\[\pm \] this sign means you have to do it two times.

Solve it once for +

and another one for -

so you should get two answers.

Answer 39

for x

Answer 40

For the example that I gave you where a=1 b=2 c=2 you get one answer for x

Answer 41

because it's a special case.

Answer 42

okay I get all that now. But the reason way I asked this question is becaues I don't know how to set it up. like I dnt know which numbers to chose at the begining. That why I wanted some one to set up all three and now thanks to you I can do the rest.

Answer 43

The thing is sometimes I have trouble too knowing how to set it up and Ive been taking math for a while now. Some people can see it really fast and some people can't. I can't so what I do is try to set up a complete square first.

(x+2)(x+1)

then I simplify it

(x+2)(x+1)= x^2 + 3x + 2
then I see what a b and c equal

Answer 44

That's how I get the general form of the equation. And if they tell me to complete the square I work backwards again.

Answer 45

x^2 + 3x + 2=0

Complete the square

Oh ok I can do it now

It's

(x+2)(x+1)

Answer 46

(x+2)(x+1)=0

See how I did it.

Answer 47

yah, I saw :)

Answer 48

at least I know how to do that now.

Answer 49

Cool I can do it faster now because I practice them a lot so if you keep doing it then sooner or later you will be able to catch them really fast.

Answer 50

Good Luck.

Answer 51

thanks , btw ur a gud teacher ;)