Question
upstudy study bank question image url

\( x ^ { 2 } + 2 x y - y ^ { 2 } ; \quad x = 3 \)

Ask by Beck George. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Substitute \( x=3 \) into the expression to get \( 9+6y-y^2 \).

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

Let’s plug \( x = 3 \) into the expression \( x^2 + 2xy - y^2 \). This gives us: \[ 3^2 + 2(3)y - y^2 = 9 + 6y - y^2 \] Now, we can rewrite the expression as: \[ -y^2 + 6y + 9 \] This is a quadratic in terms of \( y \), which opens downwards (since the coefficient of \( y^2 \) is negative). Quadratics are not only fun to explore mathematically, but they also graph out beautifully as parabolas! If you're solving or optimizing this expression, you might find it helpful to identify the vertex. The vertex of a quadratic given by \( ay^2 + by + c \) can be found using \( y = -\frac{b}{2a} \). In this case, set \( a = -1 \) and \( b = 6 \). The coordinates of the vertex will tell you the maximum point on the graph – a neat trick for visualizing your results!

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