A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

A function is defined as f(x)=ax^2+bx+d, where a, b, and d are integers. The minimum value of f(x) is -4 Determine the x-coordinate of the minimum value of f(x) and hence find the value of d.

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    okay, well you know that at some x the minimum is -4, so you can find that point by taking the derivative of f(x) and setting it to 0 which is: \[2ax +b = 0\] so \[x = -b/2a\] then you can place that in the first equation: \[ax^2 + bx + d = a(-b/2a)^2 + b(-b/2a) + d = b^2/2a -b^2/2a + d = -4\] thus \[d = -4\] then you can find x by setting f(x) = -4 and then solving for x, which gives \[-4 = ax^2 +bx -4 --> 0 = ax^2+bx = x(ax + b)\] so you can say that \[x = 0, -b/a\]

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    sorry haha, math error :O. just noticed. should be \[b^2/4a^2 - b^2/2a + d = -4\] which would change everything. its kinda late here......sorry.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    so then \[x = -b/2a\] and \[d = (-16a^2 +b^2(2a-1))/4a^2\]

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not \[4a^2\] i meant \[4/a\]....I am going to bed.

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So to actually put it together nicely. \[x=-b/2a\] and \[d = -4 - b^2/4a + b^2/2a = -4 + b^2/4a\].

  6. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.