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Math Help - Function question (easy but i dont understand)

  1. #1
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    Function question (easy but i dont understand)

    So my teacher puts this on the board and i wa.s liek WHAT, then i asked him and he didnt make any sense so i need your help guys!

    Find shaded area (Draw graph + shade)

    1) y < or equal to 4x^2, y < or equal to 6-2x, x > or equal to 0

    I have no idea what to do, could someone please help!

    Thanks alot
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  2. #2
    Senior Member mollymcf2009's Avatar
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    Hello!

    Draw all three graphs together on one xy axis. The shaded area will be the area bounded by all three functions based on the conditions given for each function. So,

    4x^2 is a parabola with its vertex at the origin and compressed towards the y axis by a factor of 4 (FYI, a coefficient > 1 on your x^2 term of a parabola makes it skinnier, a coefficient <1 makes the graph wider)

    The shaded area will be below this equation will be the entire graph except for what is inside the parabola.

    BUT, you aren't done yet!!

    Now graph the second equation right on top of the first. 6 - 2x is a line with a slope of -2 and a y-intercept of 6. Graph it and find the area where y \leq it. If the line were by itself, the entire left side of the graph of that line would be shaded. BUT!!!! Since the conditions for the parabola must also be met, the graph of the line on top of the parabola will not allow the area inside of the parabola to be shaded.

    BUT, you aren't done yet!!!

    The last condition is that x \geq 0. SOOOOO, you know what x = 0 looks like. So where on this graph satisfies all three of your given conditions?

    The area under the parabola, under the line and to the right of x=0

    Can you see it now? Hope that helps! Good luck!
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  3. #3
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    Ok thats really helpful!

    But lets go back one step!

    I dont even understand what a constraint like y < or equal to 4x^2 means!

    How do you graph it with that constraint, and what does that constraint represent!?

    Just mention that and i'll be all set!
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by I Drink and Derive View Post
    Ok thats really helpful!

    But lets go back one step!

    I dont even understand what a constraint like y < or equal to 4x^2 means!

    How do you graph it with that constraint, and what does that constraint represent!?

    Just mention that and i'll be all set!
    In this case, its the parabola y=4x^2, drawn with a solid line. Since y\leqslant 4x^2, we shade the region below the parabola (the region not shaded should be within the parabola).

    If it was y<4x^2, then its the parabola y=4x^2, drawn with a dotted line. Since y\leqslant 4x^2, we shade the region below the parabola (the region not shaded should be within the parabola).

    Does this help?
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