Determine without graphing

Determine without graphing, whether the given function has a maximum value and then find the value. f(x)=3x^2+30x-1

  1. 👍 0
  2. 👎 0
  3. 👁 59
asked by Jenn
  1. Steve had already answered this question for you.

    http://www.jiskha.com/display.cgi?id=1363360907

    What part of his answer did you not like ?

    1. 👍 0
    2. 👎 0
    posted by Reiny
  2. I needed help learning how to find the value.

    1. 👍 0
    2. 👎 0
    posted by Jenn
  3. f(x) = 3(x^2 + 10x +25)-76
    = 3(x+5)^2 -76

    The function has no maximum. It has a minimum of -76 when x = -5.

    1. 👍 0
    2. 👎 0
    posted by drwls
  4. Hmmm. I explained that there is no maximum value. Don't expect to be able to find it.

    Now, if you want to find the minimum value, try completing the square:

    3x^2+30x-1
    = 3(x^2 + 10x) - 1
    = 3(x^2 + 10x + 25) - 1 - 75
    That step is the key. We added 75 to complete the square, so we have to subtract it as well to avoid changing f(x)
    = 3(x+5)^2 - 76

    Now you can see that since (x+5)^2 is always at least zero (since squares are never negative), the smallest value for (x+5)^2 is when x = -5. In that case, f(x) = 3(0) - 76

    So, f(-5) = -76, and it can never be less than that, because whatever x is, (x+5)^2 will be some positive number, making f(x) > -76

    1. 👍 0
    2. 👎 0
    posted by Steve

Respond to this Question

First Name

Your Response

Similar Questions

  1. Algebra 2

    1. By graphing the system of constraints, find the values of x and y that maximize the objective function. 2

    asked by Fading on November 8, 2016
  2. College algebra

    Determine without graphing, whether the given function has a maximum value and then find the value. f(x)=3x^2+18x-6

    asked by Jenn on March 15, 2013
  3. algebra

    1)Identify the y-intercept and the axis of symemetry for the graph of f(x)=-3x^2+6x+12. answer=12:x=1 2)Determine whether f(x)=-5x^2-10x+6 has a maximum or minimum value and find that value. answer=maximum -1 3)Solve x^2=4x by

    asked by Marissa on August 14, 2007
  4. Pre-Calculus

    For the function f(x)=12x^3+4x^2-27x-9 describe the end behavior. Find the real zeros of f and determine whether the graph crosses or touches the x-axis at each x-intercept. Use the zeros of f and test numbers to find the

    asked by Leizy on October 10, 2015
  5. Algebra

    This will be a multiple post thing so please bear with me. If my answers are wrong then please explain I'll post my work as needed thanks. 1)Identify the y-intercept and the axis of symemetry for the graph of f(x)=-3x^2+6x+12.

    asked by Marissa on August 12, 2007
  6. pre-cal: graphs of functions- fill in the blank

    To find the domain of a function from its graph... To find the range of a function from its graph... To approximate the relative minimum or maximum of a function using a graphing utility,... Let a(,f(a)) and (b,f(b)) be two points

    asked by Anonymous on September 16, 2007
  7. Pre-Calculus

    1) Use a graphing utility to obtain the graph of the function. Give the domain of the function and identify any vertical or horizontal asymptotes. x+4/ x^2+x-6. 2) Use a graphing utility to graph the function and determine the

    asked by Addy on April 8, 2011
  8. AP Calculus

    Consider the function f(x) = 1/4x^4 - 5/3x^3 - 3/2x^2 + 15x - 3. A. Find the relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values. B. Determine

    asked by Steph on January 16, 2017
  9. Algebra2

    Complete parts a – c for each quadratic function: a. Find the y-intercept, the equation of the axis of symmetry and the x- coordinate of the vertex. b. Make a table of values that includes the vertex. c. Use this information to

    asked by Mara on February 8, 2008
  10. Math(Please help)

    Projectile motion: Let's suppose you throw a ball straight up with an initial speed of 50 feet per second from a height of feet. a) Find the equation that describes the motion as a function of time. My answer was x = 0 and

    asked by Abbey on April 16, 2010

More Similar Questions