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LaynaMae
 one year ago
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.
LaynaMae
 one year ago
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.

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triston_mccain
 one year ago
Best ResponseYou've already chosen the best response.0the answer is message me!!

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1@amistre64 @Luigi0210 @Compassionate

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1@AllTehMaffs @johnweldon1993 ?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2We'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 ??

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

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Alright no problem we'll walk through it :)

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1Oh my goodness thank you so much ..

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Okay....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?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Since 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...

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2so far we just have the 2 xintercepts...this looks like dw:1386883312282:dw

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1So is that all it's asking me to do ? :o

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Not quite...almost done though :) are you with me through what I've done so far?

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1Ehh , kind of ... It's just a lot of information

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2I 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?

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1That was a lot easier to understand :)

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Awesome! :) Okay....so now...do you know how to expand this factored form?? to make it look something like x² + bx + c

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Don't get down...this is a pretty simple process...stay with me :)

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2We 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
 one year ago
Best ResponseYou've already chosen the best response.2so..."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 :)

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1Wait fill out the first 2 question marks or the second 2 ..?

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1Ok 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
 one year ago
Best ResponseYou've already chosen the best response.2Oh so close...everything is right but what is x times x? x times x is x² right?

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1Ohhh yeah ! That makes more sense !!

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Alright perfect! so altogether we have x² + 2x  2x  4 Anything look like it can be simplified?

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1@johnweldon1993 don't leave meee we're so close to finishing thisss D:

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2lol no I'm not leaving openstudy is starting to lag on my computer...

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2So back to that question... x² + 2x  2x  4 anything that can be simplified here?

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Right! what is 2x  2x ??

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2lol 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

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Thats it :) much easier to put it in a graphing calculator! lol

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2And 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 :)

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1OMG THANK YOU SOO MUCH !! :DD

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Anytime :) I hope it all made sense!

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2And if you ever need help with anything feel free to tag me in a question or message me :)

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1I definitely will ! :)

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

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1Using 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
 one year ago
Best ResponseYou've already chosen the best response.2Oh 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...

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2For 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?

LaynaMae
 one year ago
Best ResponseYou've already chosen the best response.1So that's it ?? :o lol i'm a little slow

johnweldon1993
 one year ago
Best ResponseYou've already chosen the best response.2Yeah 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 :)
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