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LaynaMae
 2 years 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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.0the answer is message me!!

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

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

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3We'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
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.3Alright no problem we'll walk through it :)

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

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Okay....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
 2 years ago
Best ResponseYou've already chosen the best response.3Since 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
 2 years ago
Best ResponseYou've already chosen the best response.3so far we just have the 2 xintercepts...this looks like dw:1386883312282:dw

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

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Not quite...almost done though :) are you with me through what I've done so far?

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

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3I 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
 2 years ago
Best ResponseYou've already chosen the best response.1That was a lot easier to understand :)

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Awesome! :) Okay....so now...do you know how to expand this factored form?? to make it look something like x² + bx + c

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Don't get down...this is a pretty simple process...stay with me :)

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3We 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
 2 years ago
Best ResponseYou've already chosen the best response.3so..."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
 2 years ago
Best ResponseYou've already chosen the best response.1Wait fill out the first 2 question marks or the second 2 ..?

LaynaMae
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.3Oh so close...everything is right but what is x times x? x times x is x² right?

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

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Alright perfect! so altogether we have x² + 2x  2x  4 Anything look like it can be simplified?

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

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3lol no I'm not leaving openstudy is starting to lag on my computer...

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3So back to that question... x² + 2x  2x  4 anything that can be simplified here?

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Right! what is 2x  2x ??

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3lol 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
 2 years ago
Best ResponseYou've already chosen the best response.3Thats it :) much easier to put it in a graphing calculator! lol

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3And 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
 2 years ago
Best ResponseYou've already chosen the best response.1OMG THANK YOU SOO MUCH !! :DD

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Anytime :) I hope it all made sense!

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3And if you ever need help with anything feel free to tag me in a question or message me :)

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

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

LaynaMae
 2 years 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
 2 years ago
Best ResponseYou've already chosen the best response.3Oh 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
 2 years ago
Best ResponseYou've already chosen the best response.3For 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
 2 years ago
Best ResponseYou've already chosen the best response.1So that's it ?? :o lol i'm a little slow

johnweldon1993
 2 years ago
Best ResponseYou've already chosen the best response.3Yeah 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 :)

kaylaprincess
 5 months ago
Best ResponseYou've already chosen the best response.0im having trouble with a similar problem, (x+3)(x3) 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
 5 months ago
Best ResponseYou've already chosen the best response.0@mathmate @abb0t @ganeshie8 @SithsAndGiggles @zepdrix @Compassionate much appreciation for help.
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