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LaynaMae
Group Title
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.
 8 months ago
 8 months ago
LaynaMae Group Title
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.
 8 months ago
 8 months ago

This Question is Closed

triston_mccain Group TitleBest ResponseYou've already chosen the best response.0
the answer is message me!!
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
@amistre64 @Luigi0210 @Compassionate
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
@AllTehMaffs @johnweldon1993 ?
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 (xintercepts) of the function are... What value(s) of 'x' make (x  2)(x + 2) = 0 ??
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Oh God .. I have NO idea .... I don't get any of this , I had help on question 1 as well :/
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Alright no problem we'll walk through it :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Oh my goodness thank you so much ..
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 xintercepts) 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?
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 xintercept... 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 xintercept for the graph...
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
so far we just have the 2 xintercepts...this looks like dw:1386883312282:dw
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
So is that all it's asking me to do ? :o
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Not quite...almost done though :) are you with me through what I've done so far?
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Ehh , kind of ... It's just a lot of information
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 x2 had to equal 0... So that's how we solved for the 2 xintercepts... maybe a little summary better?
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
That was a lot easier to understand :)
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Awesome! :) Okay....so now...do you know how to expand this factored form?? to make it look something like x² + bx + c
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Omg no :'(
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Don't get down...this is a pretty simple process...stay with me :)
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Wait fill out the first 2 question marks or the second 2 ..?
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Both :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
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 ?
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Oh so close...everything is right but what is x times x? x times x is x² right?
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Ohhh yeah ! That makes more sense !!
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Alright perfect! so altogether we have x² + 2x  2x  4 Anything look like it can be simplified?
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
@johnweldon1993 don't leave meee we're so close to finishing thisss D:
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
lol no I'm not leaving openstudy is starting to lag on my computer...
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
So back to that question... x² + 2x  2x  4 anything that can be simplified here?
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
2x  2x ?
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Right! what is 2x  2x ??
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
0 of course :p
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 yintercept... so 4 would be this yintercept... 2 xintercepts at x = 2 and x = 2...and 1 yintercept at 4 so altogether we have a graph that looks like... dw:1386884802676:dw
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
And that's it ?? :o
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Thats it :) much easier to put it in a graphing calculator! lol
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
OMG THANK YOU SOO MUCH !! :DD
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Anytime :) I hope it all made sense!
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
And if you ever need help with anything feel free to tag me in a question or message me :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
I definitely will ! :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
I actually need help with a question following this one !! :o @johnweldon1993
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
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.
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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...
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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?
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Makes sense !
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Perfect :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
So that's it ?? :o lol i'm a little slow
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
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 :)
 8 months ago

LaynaMae Group TitleBest ResponseYou've already chosen the best response.1
Thank you againnn :)
 8 months ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.1
Of course :)
 8 months ago
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