1. If you had an old account at the OLD OLD Nexopia, you can get that account back by resetting your password.

    Click Here to Reset Your Old Account's Password.

    Alternatively, you can Register a New Account!

MATH TIME!

Discussion in 'User Topics' started by Mr.Lame, Jan 9, 2018.

  1. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    Okay, suppose we are given a parabolic function in the form:

    y = a(x - h)^2 + k, where a ≠ 0

    The vertex (for a parabola, this is the turning point) will be at (h,k). If a < 0 then the parabola will open downwards and the vertex will be at the maximum, but if 0 < a then the parabola opens upwards and the vertex will be at the minimum.

    The parabola we've been given may be written as:

    y = 1(x - 0)^2 + (-7)

    This means the vertex is at (0,-7) and the parabola opens upwards, so the minimum value is -7. Let's look at a graph of the function:

    lame001.png

    The blue curve is the parabola, and the dots on the curve represent the 4 smallest values of the parabola when x is an integer. The horizontal lines represent the value of the parabola for those integral values of x, namely:

    y = -7
    y = -6
    y = -3
    y = 2

    Does that make sense?
     
    • Love Love x 1
  2. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    Yes I remember this!!!!! so in other words I should go to my calculator for this type of question as well correct?
     
    • Like Like x 1
  3. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    You shouldn't need a calculator for this, except perhaps if you want to graph the function to get an idea what the curve looks like and how it behaves.
     
    • Like Like x 1
  4. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    Hey @MarkFL, I'm having some issues again with ABS

    I'm trying to understand why there is a minus instead of a plus |x-4|

    The distance between x and 4 is greater than 0 but less than 4.

    Is it because it's less than four?

    0<|x-4|<4
     
    • Like Like x 1
  5. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    We've got two cases to consider here...the first is:

    x - 4 ≥ 0

    Recall that when |x| = x when x ≥ 0, and |x| = -x when x < 0.

    In this case, we can write:

    0 < x - 4 < 4

    Add through by 4:

    4 < x < 8

    The second case is:

    x - 4 < 0

    In this case we may write:

    0 < 4 - x < 4

    Multiply through by -1:

    0 > x - 4 > -4

    Add through by 4:

    4 > x > 0

    And so our solution, in interval notation, is:

    (0, 4) U (4, 8)

    On the number line, this is:

    lame002.png
     
    • Winner Winner x 1
  6. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    That part makes sense I just don't understand why it's a x-4 :/ instead of x+4
     
  7. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    Thought abs was suppose to be positive inside!
     
  8. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    The distance between x and 4 is the magnitude of the difference between x and 4. For a difference we use subtraction, and for a magnitude we use absolute value, thus the distance d between x and 4 on the number line is:

    d = |x - 4|
     
    • Love Love x 1
  9. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    Interesting was trying to solve got everything except mixed up the sign and didn't know why T.T
     
  10. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    No, the actual absolute value is never negative, we always have:

    0 ≤ |x|

    But the value of x itself can be any real number. If x is negative then:

    |x| = -x

    If x is non-negative, then:

    |x| = x

    For example, if we have:

    |-2|

    Then we see -2 < 0 and so:

    |-2| = -(-2) = 2
     
    • Love Love x 1
  11. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    Sweet :D . I'll have more for you soon! Hahaha
     
    • Love Love x 1
  12. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    With your help @MarkFL I feel like I can obtain my 4.0 GPA :D
     
    • Winner Winner x 1
  13. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    @MarkFL Okay my brain hurts I feel like I'm making a small error.

    Simplify the variable equation:
    3/4(5a+2)-1/2(3a-5)

    Now I found the LCD to get rid of the fractions but I feel that's not what I was suppose to do... (I have the answer :rofl: ). helppp meeee pleassseee <3
     
  14. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    Is this the expression?

    lame003.png
     
  15. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    Nope, it's fractions on the outside of the brackets! Where do you get this images? I'll capture the questions lol
     
  16. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    I'm using my local server where I have a vB site running LaTeX powered by MathJax.

    lame004.png
     
    • Winner Winner x 1
  17. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    Snap that was awesome, yeah it's 9/4a+4
     
    • Love Love x 1
  18. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    So I almost had it right I should have just timesed the fractions instead of everything.
     
  19. MarkFL

    MarkFL La Villa Strangiato Staff Member Mod Squad

    Blogs:
    0
    Joined:
    Nov 30, 2017
    Posts:
    2,496
    Likes Received:
    984
    Yeah, if you distribute the 1/4 then you do get (9/4)a + 4. :)

    I actually prefer the first form I gave. ;)
     
    • Winner Winner x 1
  20. Mr.Lame

    Mr.Lame Regular

    Blogs:
    28
    Joined:
    Dec 7, 2009
    Posts:
    799
    Likes Received:
    367
    @MarkFL
    Having some issues with this one, I don't know why it looks really easy

    16t^2+80t+4

    t=2

    I'm ending up going the easy way on this but should I be using quadratic equation? Ending up with 228....
     

Share This Page