MATH TIME!

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

  1. MarkFL

    MarkFL Guest

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    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?
     
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  2. Mr.Lame

    Mr.Lame Veteran

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    Yes I remember this!!!!! so in other words I should go to my calculator for this type of question as well correct?
     
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  3. MarkFL

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    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.
     
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  4. Mr.Lame

    Mr.Lame Veteran

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    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
     
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  5. MarkFL

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    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
     
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  6. Mr.Lame

    Mr.Lame Veteran

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    That part makes sense I just don't understand why it's a x-4 :/ instead of x+4
     
  7. Mr.Lame

    Mr.Lame Veteran

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    Thought abs was suppose to be positive inside!
     
  8. MarkFL

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    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|
     
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  9. Mr.Lame

    Mr.Lame Veteran

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    Interesting was trying to solve got everything except mixed up the sign and didn't know why T.T
     
  10. MarkFL

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    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
     
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  11. Mr.Lame

    Mr.Lame Veteran

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    Sweet :D . I'll have more for you soon! Hahaha
     
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  12. Mr.Lame

    Mr.Lame Veteran

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    With your help @MarkFL I feel like I can obtain my 4.0 GPA :D
     
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  13. Mr.Lame

    Mr.Lame Veteran

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    @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

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    Is this the expression?

    lame003.png
     
  15. Mr.Lame

    Mr.Lame Veteran

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    Nope, it's fractions on the outside of the brackets! Where do you get this images? I'll capture the questions lol
     
  16. MarkFL

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    I'm using my local server where I have a vB site running LaTeX powered by MathJax.

    lame004.png
     
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  17. Mr.Lame

    Mr.Lame Veteran

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    Snap that was awesome, yeah it's 9/4a+4
     
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  18. Mr.Lame

    Mr.Lame Veteran

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    So I almost had it right I should have just timesed the fractions instead of everything.
     
  19. MarkFL

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    Yeah, if you distribute the 1/4 then you do get (9/4)a + 4. :)

    I actually prefer the first form I gave. ;)
     
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  20. Mr.Lame

    Mr.Lame Veteran

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    @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....
     

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