anonymous
  • anonymous
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.
Algebra
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
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anonymous
  • anonymous
the answer is message me!!
anonymous
  • anonymous
@amistre64 @Luigi0210 @Compassionate

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anonymous
  • anonymous
@AllTehMaffs @johnweldon1993 ?
johnweldon1993
  • johnweldon1993
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 ??
anonymous
  • anonymous
Oh God .. I have NO idea .... I don't get any of this , I had help on question 1 as well :/
johnweldon1993
  • johnweldon1993
Alright no problem we'll walk through it :)
anonymous
  • anonymous
Oh my goodness thank you so much ..
johnweldon1993
  • johnweldon1993
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?
johnweldon1993
  • johnweldon1993
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...
johnweldon1993
  • johnweldon1993
so far we just have the 2 x-intercepts...this looks like |dw:1386883312282:dw|
anonymous
  • anonymous
So is that all it's asking me to do ? :o
johnweldon1993
  • johnweldon1993
Not quite...almost done though :) are you with me through what I've done so far?
anonymous
  • anonymous
Ehh , kind of ... It's just a lot of information
johnweldon1993
  • johnweldon1993
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?
anonymous
  • anonymous
That was a lot easier to understand :)
johnweldon1993
  • johnweldon1993
Awesome! :) Okay....so now...do you know how to expand this factored form?? to make it look something like x² + bx + c
anonymous
  • anonymous
Omg no :'(
johnweldon1993
  • johnweldon1993
Don't get down...this is a pretty simple process...stay with me :)
johnweldon1993
  • johnweldon1993
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
johnweldon1993
  • johnweldon1993
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 :)
anonymous
  • anonymous
Wait fill out the first 2 question marks or the second 2 ..?
johnweldon1993
  • johnweldon1993
Both :)
anonymous
  • anonymous
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 ?
johnweldon1993
  • johnweldon1993
Oh so close...everything is right but what is x times x? x times x is x² right?
anonymous
  • anonymous
Ohhh yeah ! That makes more sense !!
johnweldon1993
  • johnweldon1993
Alright perfect! so altogether we have x² + 2x - 2x - 4 Anything look like it can be simplified?
anonymous
  • anonymous
@johnweldon1993 don't leave meee we're so close to finishing thisss D:
johnweldon1993
  • johnweldon1993
lol no I'm not leaving openstudy is starting to lag on my computer...
johnweldon1993
  • johnweldon1993
So back to that question... x² + 2x - 2x - 4 anything that can be simplified here?
anonymous
  • anonymous
2x - 2x ?
johnweldon1993
  • johnweldon1993
Right! what is 2x - 2x ??
anonymous
  • anonymous
0 of course :p
johnweldon1993
  • johnweldon1993
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... |dw:1386884802676:dw|
anonymous
  • anonymous
And that's it ?? :o
johnweldon1993
  • johnweldon1993
Thats it :) much easier to put it in a graphing calculator! lol
johnweldon1993
  • johnweldon1993
And it's good because everything we just did...will act as your explanation of what the key features of your graph are...the x and y intercepts :)
anonymous
  • anonymous
OMG THANK YOU SOO MUCH !! :DD
johnweldon1993
  • johnweldon1993
Anytime :) I hope it all made sense!
johnweldon1993
  • johnweldon1993
And if you ever need help with anything feel free to tag me in a question or message me :)
anonymous
  • anonymous
I definitely will ! :)
anonymous
  • anonymous
I actually need help with a question following this one !! :o @johnweldon1993
anonymous
  • anonymous
Using your graph from question 4, describe if the average rate of change is increasing or decreasing, from left to right. Justify your observations with calculations.
johnweldon1993
  • johnweldon1993
Oh sorry, didn't give me the notification you replied here... Well lets see...from (-infinity to 0) the function is decreasing....and from (0 to +infinity) the function is increasing...
anonymous
  • anonymous
Right :o
johnweldon1993
  • johnweldon1993
For the justification part... \[\large \frac{f(x_2) - f(x_1)}{x_2 - x_1}\] so say that from x = -4 to x = -1 we have f(x) = x² - 4 remember? so plug in x = -4 and x = -1 to that to get f(x2) and f(x1) f(x2) = -1² - 4 = -3 f(x1) = -4² - 4 = 12 so \[\large \frac{-3 - 12}{-1 + 4}\] \[\large \frac{-15}{3}\] \[\large -5 \] since this is a negative number we have a decreasing interval... make sense?
anonymous
  • anonymous
Makes sense !
johnweldon1993
  • johnweldon1993
Perfect :)
anonymous
  • anonymous
So that's it ?? :o lol i'm a little slow
johnweldon1993
  • johnweldon1993
Yeah that's it...if you wanted to do another calculation for the positive side you could but....yeah lol...and you're not slow you got exactly what I was saying :)
anonymous
  • anonymous
Thank you againnn :)
johnweldon1993
  • johnweldon1993
Of course :)
kaylaprincess
  • kaylaprincess
im having trouble with a similar problem, (x+3)(x-3) x = 3 y = -9 I have graphed. i just dont understand : describe if the average rate of change is increasing or decreasing, from left to right. Justify your observations with calculations. like how do i do/start this?
kaylaprincess
  • kaylaprincess
@mathmate @abb0t @ganeshie8 @SithsAndGiggles @zepdrix @Compassionate much appreciation for help.

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