Question
upstudy study bank question image url

Write the equation of a quadratic function with the given solutions. Use standard form \( f(x)=a x^{2}+b x+c \) \( x=2 \) and \( x=1 \) Show your work here Hint: To add an exponent \( \left(x^{y}\right) \), type "exponent" or press " \( \wedge \) "

Ask by Bates Bernard. in the United States
Mar 15,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The quadratic function with solutions \(x=2\) and \(x=1\) is \[ f(x) = x^2 - 3x + 2 \]

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Bonus Knowledge

To find the quadratic function with solutions \( x = 2 \) and \( x = 1 \), we start with the fact that if \( x = p \) and \( x = q \) are solutions, then the quadratic can be expressed as: \[ f(x) = a(x - p)(x - q) \] Plugging in our solutions, we have: \[ f(x) = a(x - 2)(x - 1) \] Expanding this, we get: \[ f(x) = a[(x - 2)(x - 1)] = a(x^2 - 3x + 2) \] Now, to express it in standard form \( f(x) = ax^2 + bx + c \), we simply distribute \( a \): \[ f(x) = ax^2 - 3ax + 2a \] For \( a = 1 \) (to keep it simple), the quadratic function becomes: \[ f(x) = x^2 - 3x + 2 \] Thus, \( f(x) = x^2 - 3x + 2 \) is the quadratic function in standard form with the given solutions. Check your work: The solutions can be found by setting \( f(x) = 0 \) and factoring: \[ (x - 2)(x - 1) = 0 \] This hence confirms the solutions are indeed \( x = 2 \) and \( x = 1 \).

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy