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Math Help - [SOLVED] Quadratics and Co-ordinate Geometry

  1. #1
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    Cool [SOLVED] Quadratics and Co-ordinate Geometry

    The equation of the curve is y=8x-x^2

    Q) Find the coordinates of the stationary point of the curve.

    I know that I am supposed to express this equation in the form a-(x+b)^2 and then get the values of b for x and a for y to get the answer. But what are stationary points? Is that the vertex?

    Q) Find the set of values of x for which y is greater than equal to -20

    I've got the final answer

    (x+2)(x-10) is less than or equal to 0

    x= -2 or x= 10

    Now what I don't understand is what is the sketch method? And how to easily find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x.

    Thanks a lot in advance.
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  2. #2
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    Quote Originally Posted by unstopabl3 View Post
    The equation of the curve is y=8x-x^2

    Q) Find the coordinates of the stationary point of the curve.

    I know that I am supposed to express this equation in the form a-(x+b)^2 and then get the values of b for x and a for y to get the answer. But what are stationary points? Is that the vertex?

    Q) Find the set of values of x for which y is greater than equal to -20

    I've got the final answer

    (x+2)(x-10) is less than or equal to 0

    x= -2 or x= 10

    Now what I don't understand is what is the sketch method? And how to easily find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x.

    Thanks a lot in advance.
    HI

    (1) You can use differentiation or complete the square like you did . Yes , its vertex .. or in other words max or min points .

    (2) Ok .. (x-10)(x+2)\leq0

    You will get a U shaped graph where it intersects x=10 and x=-2 .

    y is less than or equals 0 ... so the solution part will be the lower part of the U graph because the lower part of the graph has all its values of y lesser than 0 ..

    Did i make things confusing for you ?
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  3. #3
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    Thanks for the quick reply, I am still confused about Q#2

    Can you please explain a bit more on how to find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x. Do you understand what I mean?
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  4. #4
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    Quote Originally Posted by unstopabl3 View Post
    Thanks for the quick reply, I am still confused about Q#2

    Can you please explain a bit more on how to find out which of the two (-2 or 10) is less than or equal to x or which one is greater than or equal to x. Do you understand what I mean?
    Do you know how to sketch the graph ? When the inequality is \leq0 or <0 , then the solution will be the bottom part of the graph and if the inequality is \geq0 or >0 , then the solution will be the top part of the graph .

    If you still don get me , then this is an alternative method .

    since the inequality is \leq 0 , then one of the factors must be negative and the other one will be positive . Since you do not know which is which , so you will need to solve for 2 cases .. ie

    x-10\leq0 , x+2\geq0 --- case 1

    x-10\geq0 , x+2\leq 0 --- case 2

    Then draw a number line with these points and find the intersection .
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  5. #5
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    Cool

    Thanks, I got it now
    Really appreciate you 'dumbing' it down for me
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