Results 1 to 2 of 2

Math Help - Quadratic Expressions and equations

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    66

    Question Quadratic Expressions and equations

    Given that y = 5 + px - (x^2) = 9 - (x+q)^2 , where q > 0, for all values of x,

    a) calculate the values of the constants p and q.

    b) state the maximum value of y and the value of x at which it occurs.

    c) find the set of value of x for which y is negative.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by Ilsa View Post
    Given that y = 5 + px - (x^2) = 9 - (x+q)^2 , where q > 0, for all values of x,

    a) calculate the values of the constants p and q.

    b) state the maximum value of y and the value of x at which it occurs.

    c) find the set of value of x for which y is negative.
    to a):

    According to the text of the question

    -x^2+px+5 = -x^2-2qx-q^2+9

    Compare the co-efficients and solve the system of equations for p and q:

    \left|\begin{array}{rcl}p&=&-2q \\ 5&=&-q^2+9\end{array}\right.

    You should come out with p = -4 and q = 2 (the negative solution of q is not allowed).

    Thus the quadratic function has the equation: y = -x^2-4x+5

    to b): Determine the vertex of the parabola by completing the square.

    to c) Determine the zeros of the function and consequently those intervals where y < 0.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. quadratic expressions
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 7th 2011, 04:12 PM
  2. Replies: 16
    Last Post: October 31st 2010, 06:39 AM
  3. Find expressions for the quadratic functions
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: January 25th 2010, 03:43 AM
  4. Replies: 7
    Last Post: September 10th 2009, 03:07 PM
  5. Rational Expressions & Quadratic Formula Help
    Posted in the Algebra Forum
    Replies: 3
    Last Post: August 31st 2007, 10:45 AM

Search Tags


/mathhelpforum @mathhelpforum