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LaynaMae
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.
the answer is message me!!
@amistre64 @Luigi0210 @Compassionate
@AllTehMaffs @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 ??
Oh God .. I have NO idea .... I don't get any of this , I had help on question 1 as well :/
Alright no problem we'll walk through it :)
Oh my goodness thank you so much ..
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?
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...
so far we just have the 2 x-intercepts...this looks like |dw:1386883312282:dw|
So is that all it's asking me to do ? :o
Not quite...almost done though :) are you with me through what I've done so far?
Ehh , kind of ... It's just a lot of information
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?
That was a lot easier to understand :)
Awesome! :) Okay....so now...do you know how to expand this factored form?? to make it look something like x² + bx + c
Don't get down...this is a pretty simple process...stay with me :)
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
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 :)
Wait fill out the first 2 question marks or the second 2 ..?
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 ?
Oh so close...everything is right but what is x times x? x times x is x² right?
Ohhh yeah ! That makes more sense !!
Alright perfect! so altogether we have x² + 2x - 2x - 4 Anything look like it can be simplified?
@johnweldon1993 don't leave meee we're so close to finishing thisss D:
lol no I'm not leaving openstudy is starting to lag on my computer...
So back to that question... x² + 2x - 2x - 4 anything that can be simplified here?
Right! what is 2x - 2x ??
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|
Thats it :) much easier to put it in a graphing calculator! lol
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 :)
OMG THANK YOU SOO MUCH !! :DD
Anytime :) I hope it all made sense!
And if you ever need help with anything feel free to tag me in a question or message me :)
I definitely will ! :)
I actually need help with a question following this one !! :o @johnweldon1993
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.
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...
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?
So that's it ?? :o lol i'm a little slow
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 :)
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?
@mathmate @abb0t @ganeshie8 @SithsAndGiggles @zepdrix @Compassionate much appreciation for help.