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Solving for the X Intercepts

  1. Jun 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Sketch the graph of each function given using shifts and stretches of the parent function y=x2 (not by simply plotting points). Clearly indicate and explicitly state the orientation, vertex, axis of symmetry, y-intercept, and point symmetric to the y-intercept, the x-intercepts, and the maximum or minimum value of each function. Use these features to complete your graph.

    f(x)=-x2-4x



    2. Relevant equations



    3. The attempt at a solution
    My factoring(plz check):
    f(x)=-x2-4x
    f(x)=-(x2-4x+4)+4=0
    f(x)=-(x-2)2+4=0.
    Finding the x intercepts is the part I am stuck on.

    The y intercept is obviously 0, so we have 0,0.
    I know that the other x intercept will be at 4 due to the similar proportion (I think) but I want to know how to find that.

    We get -4=-(x-2)2
    +-SQRT(-4)=-x+2
    -x=-2+-SQRT(-4)
    X=2+-SQRT(-4)

    That's a non real answer. Please someone check my math on solving for the x intercept. The rest of the problem I have done.
     
  2. jcsd
  3. Jun 14, 2009 #2

    statdad

    User Avatar
    Homework Helper

    Here's a hint: look very, very, very, closely, at the signs inside parentheses going from the first row to the second in your work (duplicated below)

    [tex]
    \begin{align*}
    f(x) & = -x^2 - 4x \\
    f(x) & = - \left(x^2 - 4x + 4\right) + 4 = 0
    \end{align*}
    [/tex]

    Also, to be mathematically correct, you should hold off on the " = 0 " portion until you've finished re-writing [tex] f(x) [/tex]
    as you want to. After the re-writing, set the new form equal to zero and solve.
     
  4. Jun 14, 2009 #3
    Got it, thanks! :) Answer my next thread please- lol.
     
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