calculus

posted by .

Quadratic function written in standard form where a, b, and c are constants such that a is not zero.
f(x)= ax^2+bx+c

Using calculus find the vertex of the parabola formed by this quadratic function. Determine under what conditions this vertex is a maximum or minumum (using Calculus techniques). Show work using derivatives to justify our conclusions.

THis is what I did so far, but can't figure out the rest.

f'(x)= 2ax + b
0=2ax+b
-b = 2ax
-b/2a = x

Please help and show steps so that I can understand.

  • calculus -

    That is correct. The minimum ofr maximum (vertex) is at x = -b/2a
    You already know that from the quadratic equation. x = -b/2a +/- (b/2a)sqrt (b^2-4ac)
    Now
    if x = -b/2a
    what is y?
    y = a (b^2/4a^2) + b(-b/2a) + c
    = b^2/4a -b^2/2a + c
    = -b^2/4a+c

    for max or min
    f" = 2 a
    if a is +, that is a minimum
    if a is -, that is a maximum

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Algebra

    Can you please help me with the following problems?
  2. Algebra

    Please check my answers. Find the coordinates of the vertex for the parabola defined by the given quadratic function. 1.f(x) = (x - 4)2 - 4 -I got (4,-4) Find the axis of symmetry of the parabola defined by the given quadratic function. …
  3. Algebra

    Please check my answers. Find the coordinates of the vertex for the parabola defined by the given quadratic function. 1.f(x) = (x - 4)2 - 4 -I got (4,-4) Find the axis of symmetry of the parabola defined by the given quadratic function. …
  4. Algebra Problems

    Please check my answers. Find the coordinates of the vertex for the parabola defined by the given quadratic function. 1.f(x) = (x - 4)2 - 4 -I got (4,-4) Find the axis of symmetry of the parabola defined by the given quadratic function. …
  5. Math: Parabola, Vertex

    Find the vertex of the parabola associated with the quadratic function. f(x)= -1/7x^2 - 2/11x + 1/121 (h,k)= What is the vertex of this quadratic function?
  6. pre calculus

    Determine the quadratic function in vertex form (A) vertex at (-3,-10) passing through the point (2,-5) Dow do I figure it out?
  7. Pre-Calculus

    Determine a quadratic function in vertex form given each set of characteristics. * minimum value of -24 and x-intercepts at -21 and -5 I have: (-21,0) and (-5,0) How would I find the x-coordinate of the vertex?
  8. algebra 2

    A quadratic equation can be written in vertex form or in standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why a. factor …
  9. Algebra2

    A quadratic equation can be written in vertex form or in standard form. Sometimes one form is more beneficial than the other. Identify which form would be more helpful if you needed to do each task listed below and explain why. a- …
  10. Algebra 1

    The roots of a quadratic equation are -1 and -5, and a=1. A.) What are the factors of the quadratic expression?

More Similar Questions