Question

ANYONE ?? Graphing Quadratics HELPP !
(Question 1 and answer is attached)

Graph one of your 2nd degree functions from question 1. Identify which function you used and the key features of your graph. Explain how to find them algebraically.

Answer 1

the answer is message me!!

Answer 2

@amistre64 @Luigi0210 @Compassionate

Answer 3

@AllTehMaffs @johnweldon1993 ?

Answer 4

We'll work with the f(x)

f(x) = (x - 2)(x + 2)

Alright it's important to remember this is the FACTORED version of a function...what this shows is where the zeros (x-intercepts) of the function are...

What value(s) of 'x' make (x - 2)(x + 2) = 0 ??

Answer 5

Oh God .. I have NO idea .... I don't get any of this , I had help on question 1 as well :/

Answer 6

Alright no problem we'll walk through it :)

Answer 7

Oh my goodness thank you so much ..

Answer 8

Okay....so we have

f(x) = (x - 2)(x + 2)

Like I said above...seeing a function in this factored form...lets us find out where the zeros (also known as the x-intercepts) of the graph are...

This is done by setting this form = to 0...so

(x - 2)(x + 2) = 0

Okay...we know that anything times 0 = 0 right?

Answer 9

Since we know...we can see that there are 2 values of 'x' that would make this function = 0...

(x - 2)(x + 2) = 0

Well...we know that if x = 2....

(2 - 2)(2 + 2) = 0
( 0) (4) = 0
Well indeed as we know 0 times 4 DOES = 0...so x = 2 would be one x-intercept...

To find the other...if x = -2 we have

(-2 - 2)(-2 + 2) = 0
( -4 ) (0) = 0
Again it is true that -4 times 0 = 0...so -2 is ANOTHER x-intercept for the graph...

Answer 10

so far we just have the 2 x-intercepts...this looks like

Answer 11

So is that all it's asking me to do ? :o

Answer 12

Not quite...almost done though :)

are you with me through what I've done so far?

Answer 13

Ehh , kind of ... It's just a lot of information

Answer 14

I know, trying to explain it well :/ lol

just try to remember in this factored form...set the equation = to 0....and solve for 'x'

(x + 2)(x - 2) = 0

We knew either x+2 had to equal 0...
or we know that x-2 had to equal 0...

So that's how we solved for the 2 x-intercepts...

maybe a little summary better?

Answer 15

That was a lot easier to understand :)

Answer 16

Awesome! :)

Okay....so now...do you know how to expand this factored form?? to make it look something like

x² + bx + c

Answer 17

Omg no :'(

Answer 18

Don't get down...this is a pretty simple process...stay with me :)

Answer 19

We have...

(x - 2)(x + 2)

in order to expand this to a quadratic function...we use the FOIL method...

it says...

Take the first term in the first parenthesis...and multiply it by each term in the second parenthesis...
Redo this with the second term in the first parenthesis...

Sound understandable? I'm going to do it out anyways lol

Answer 20

so..."Take the first term in the first parenthesis...and multiply it by each term in the second parenthesis..."

The first term in the first parenthesis (x - 2) is 'x' right? So we multiply it by each term in the second parenthesis (x + 2)

so

x times x = ?
x times 2 = ?

Now we just redo this for the second term in the first parenthesis (x - 2) which would be -2

so

-2 times x = ?
-2 times 2 = ?

Fill in those question marks for me :)

Answer 21

Wait fill out the first 2 question marks or the second 2 ..?

Answer 22

Both :)

Answer 23

Ok well the first 2 are: x times x = 1 ? and x times 2 = 2x ?
Second 2: -2 times x = -2x ? and -2 times 2 = -4 ?

Answer 24

Oh so close...everything is right but what is x times x?

x times x is x² right?

Answer 25

Ohhh yeah ! That makes more sense !!

Answer 26

Alright perfect!

so altogether we have

x² + 2x - 2x - 4

Anything look like it can be simplified?

Answer 27

@johnweldon1993 don't leave meee we're so close to finishing thisss D:

Answer 28

lol no I'm not leaving openstudy is starting to lag on my computer...

Answer 29

So back to that question...

x² + 2x - 2x - 4

anything that can be simplified here?

Answer 30

2x - 2x ?

Answer 31

Right! what is 2x - 2x ??

Answer 32

0 of course :p

Answer 33

lol making sure you're paying attention :P

Okay...so finally we just have

x² - 4

Well...this is all we needed...because when we have a constant number in a quadratic...this is the y-intercept... so -4 would be this y-intercept...

2 x-intercepts at x = -2 and x = 2...and 1 y-intercept at -4

so altogether we have a graph that looks like...