Question
upstudy study bank question image url

ise 9 Let \( h(x)=x^{2}-4 x-c \). a) Find a nonzero value for c such that \( h(c)=c \). b) Find and simplify \( h(x-2) \) and \( h(x+a) \). Use the c-value found in part (a). Solution (b) \( h(x-2) \) h(x)=x \( 2-4 x-6 \) \[ h(x)=x^{2}-4 x-c \] \[ h(x+a) \] \[ (x-2)^{2}=(x-2) x \] such that \( \overparen{h(c)}=C \) \[ \begin{array}{l} h(x+a) \\ h(x-2)=(x-2)^{2}-4(x-2)-6 \end{array} \] \[ x \rightarrow x-2 \] \( h(x-2)=x^{2}-2 \cdot x \cdot 2+2^{2}-4 x+8-6 \) apply \( (a-b)^{2}=0 \) quachatic eq. \( \begin{array}{c}\text { Applying the } \theta \text { - } \\ \text { Property }\end{array} \) \( \Rightarrow c=0 \) or \( c-6=0 \) \( c=6 \) \( =0 \) Factoring Method Applying the 0 -factor \( \ln (x-2)=x^{2}-8 x+6 \) \[ \overbrace{\substack{ \\h(x+a) \\ x \rightarrow x+a}}^{\ln (x-2)=x-0 x+\infty}(x+a)^{2}-4(a+8)-6 \]

Ask by Davey Kirk. in the United States
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

**a)** The value of \( c \) is 6. **b)** - \( h(x-2) = x^2 - 8x + 6 \) - \( h(x+a) = x^2 + (2a - 4)x + (a^2 - 4a - 6) \)

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

Mind Expander

Let’s dive into the fascinating history of quadratics! The quadratic equation, particularly of the form \(ax^2 + bx + c = 0\), has been around since ancient times, with mathematicians like Babylonian scholars using geometric methods to solve specific cases over 4,000 years ago. Fast forward to the 17th century, and we see giants like Descartes and Fermat making strides that established the foundations of modern algebra. Isn’t it amazing how these equations have shaped mathematics through the ages? Now, let’s talk about real-world applications! Quadratic equations pop up in various fields, including physics, engineering, and finance. For instance, they are essential in calculating the trajectory of objects in motion—think of throwing a ball or launching a rocket! Additionally, businesses use quadratics to model profit maximization and cost analysis. Understanding how quadratics function can provide invaluable insights into getting things just right in the real world!

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