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Math Help - Parabol Questions

  1. #1
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    Post Parabol Questions

    Question1:  g(x)=x^2+5x+3+m is the equation of the symmetry with respect to y axis of f(x)=x^2-5x+4 ,find m
    Question2: If f:RtoR and f(x)=x^2-(3k-5)x+m+4 are given. Find the area of the triangle which is bounded by the symmetry axis of f(x),the line y=-x and the Ox axis. Thanks in advance for the solution of these questions.
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  2. #2
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    Quote Originally Posted by JohnDoe View Post
    Question1:  g(x)=x^2+5x+3+m is the equation of the symmetry with respect to y axis of f(x)=x^2-5x+4 ,find m
    Question2: If f:RtoR and f(x)=x^2-(3k-5)x+m+4 are given. Find the area of the triangle which is bounded by the symmetry axis of f(x),the line y=-x and the Ox axis. Thanks in advance for the solution of these questions.
    Q1: The y-intercept of f is a fixed point of the reflection about the y-axis. Therefore the point (0, 4) belongs to the graph of g too:

    g(0)=3+m = 4 ~\implies~m = 1

    Q2: Do you use the value of m from Q1 in this question too? And what does this mean?: Ox
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  3. #3
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    Q2 doesn't have any relation with Q1 they are totally apart and i think Ox is y=0 line.
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  4. #4
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    Quote Originally Posted by JohnDoe
    [snip]
    Question2: If f:RtoR and f(x)=x^2-(3k-5)x+m+4 are given. Find the area of the triangle which is bounded by the symmetry axis of f(x),the line y=-x and the Ox axis. Thanks in advance for the solution of these questions.
    There are a number of ways of showing that

    the symmetry axis is the vertical line x = \frac{3k-5}{2}.

    Each way finds the x-coordinate of the turning point of the given parabola.

    The area of a triangle is \frac{1}{2} \text{ base} \times \text{height}.

    A simple sketch graph shows that:

    The base of the triangle is \left| \frac{3k - 5}{2} \right|.

    The height of the triangle is \left| -\left(\frac{3k - 5}{2} \right) \right| = \left| \frac{5 - 3k}{2} \right| .

    You need magnitudes because \frac{3k - 5}{2} can be positive or negative depending on the value of k ......
    Last edited by mr fantastic; February 16th 2008 at 12:24 PM. Reason: removed a [math] to fix an expression
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