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Math Help - differential calculus

  1. #1
    fiordalisa
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    differential calculus

    Hi everyone!
    I know this is probably a pretty easy question but I'm having a mental block at the minute...
    Anyway the question is: "Show that the curves C1 and C2 intersect at the points (-2,16) and (1,7)"
    C1 : y= -x^2 - 4x +12
    C2 : y= 5x^2 + 2x

    N.B. I'm new to the forums and wasn't sure how to write "squared" so in case I got it wrong "^2" = squared

    Thanks in advance!
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by fiordalisa View Post
    Hi everyone!
    I know this is probably a pretty easy question but I'm having a mental block at the minute...
    Anyway the question is: "Show that the curves C1 and C2 intersect at the points (-2,16) and (1,7)"
    C1 : y= -x^2 - 4x +12
    C2 : y= 5x^2 + 2x

    N.B. I'm new to the forums and wasn't sure how to write "squared" so in case I got it wrong "^2" = squared

    Thanks in advance!
    If they intersect, they will have the same x value and y value (see attached graph of the two functions.) So plug the x value into both equations, if they have the same y value, then they intersect at that point.

    Test x=-2
    \begin{array}{rl}C1: y&= -(-2)^2 - 4(-2) +12\\<br />
&= -(4) - (-8) +12\\<br />
&= -4 + 8 +12\\<br />
&= 16\\\end{array}

    \begin{array}{rl}C1: y&= 5(-2)^2 + 2(-2)\\<br />
&= 5(4) + (-4)\\<br />
&= 20 -4\\<br />
&= 16\\\end{array}

    Therefore they each pass through the point (-2,16) And thus intersect at that point.

    You try the second one.
    Attached Thumbnails Attached Thumbnails differential calculus-intersecting.jpg  
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  3. #3
    Member
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    Quote Originally Posted by fiordalisa View Post
    Hi everyone!
    I know this is probably a pretty easy question but I'm having a mental block at the minute...
    Anyway the question is: "Show that the curves C1 and C2 intersect at the points (-2,16) and (1,7)"
    C1 : y= -x^2 - 4x +12
    C2 : y= 5x^2 + 2x

    N.B. I'm new to the forums and wasn't sure how to write "squared" so in case I got it wrong "^2" = squared

    Thanks in advance!
    When you want to find the intersection of two functions, you can set them equal to each other and solve for x. Then plug the x values you get back into either original function and you will get your y values.

    y= -x^2 - 4x +12
    y= 5x^2 + 2x

    both equal y, so make them equal to each other:
    -x^2 - 4x +12 = 5x^2 + 2x

    collect like terms on one side:
    -6x^2-6x+12=0

    now factor:
    -6(x^2+x-2)=0
    x^2+x-2=0
    (x+2)(x-1)=0
    x=-2 or x=1

    ....then plug in.
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