## 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.

1. LaynaMae

2. triston_mccain

3. LaynaMae

@amistre64 @Luigi0210 @Compassionate

4. LaynaMae

@AllTehMaffs @johnweldon1993 ?

5. 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 ??

6. LaynaMae

Oh God .. I have NO idea .... I don't get any of this , I had help on question 1 as well :/

7. johnweldon1993

Alright no problem we'll walk through it :)

8. LaynaMae

Oh my goodness thank you so much ..

9. 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?

10. 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...

11. johnweldon1993

so far we just have the 2 x-intercepts...this looks like |dw:1386883312282:dw|

12. LaynaMae

So is that all it's asking me to do ? :o

13. johnweldon1993

Not quite...almost done though :) are you with me through what I've done so far?

14. LaynaMae

Ehh , kind of ... It's just a lot of information

15. 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?

16. LaynaMae

That was a lot easier to understand :)

17. johnweldon1993

Awesome! :) Okay....so now...do you know how to expand this factored form?? to make it look something like x² + bx + c

18. LaynaMae

Omg no :'(

19. johnweldon1993

Don't get down...this is a pretty simple process...stay with me :)

20. 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

21. 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 :)

22. LaynaMae

Wait fill out the first 2 question marks or the second 2 ..?

23. johnweldon1993

Both :)

24. LaynaMae

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 ?

25. johnweldon1993

Oh so close...everything is right but what is x times x? x times x is x² right?

26. LaynaMae

Ohhh yeah ! That makes more sense !!

27. johnweldon1993

Alright perfect! so altogether we have x² + 2x - 2x - 4 Anything look like it can be simplified?

28. LaynaMae

@johnweldon1993 don't leave meee we're so close to finishing thisss D:

29. johnweldon1993

lol no I'm not leaving openstudy is starting to lag on my computer...

30. johnweldon1993

So back to that question... x² + 2x - 2x - 4 anything that can be simplified here?

31. LaynaMae

2x - 2x ?

32. johnweldon1993

Right! what is 2x - 2x ??

33. LaynaMae

0 of course :p

34. 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|

35. LaynaMae

And that's it ?? :o

36. johnweldon1993

Thats it :) much easier to put it in a graphing calculator! lol

37. 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 :)

38. LaynaMae

OMG THANK YOU SOO MUCH !! :DD

39. johnweldon1993

Anytime :) I hope it all made sense!

40. johnweldon1993

And if you ever need help with anything feel free to tag me in a question or message me :)

41. LaynaMae

I definitely will ! :)

42. LaynaMae

I actually need help with a question following this one !! :o @johnweldon1993

43. LaynaMae

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.

44. 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...

45. LaynaMae

Right :o

46. 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?

47. LaynaMae

Makes sense !

48. johnweldon1993

Perfect :)

49. LaynaMae

So that's it ?? :o lol i'm a little slow

50. 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 :)

51. LaynaMae

Thank you againnn :)

52. johnweldon1993

Of course :)