Question
upstudy study bank question image url

3. \( y=-3 x^{2}+12 x+2 \)

Ask by Schofield Munoz. in the Philippines
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The quadratic function \( y = -3x^2 + 12x + 2 \) has a vertex at \( (2, 14) \), an axis of symmetry at \( x = 2 \), a y-intercept at \( (0, 2) \), and x-intercepts at \( \left(2 - \frac{\sqrt{42}}{3}, 0\right) \) and \( \left(2 + \frac{\sqrt{42}}{3}, 0\right) \).

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

The Deep Dive

Did you know that the equation \( y=-3x^2+12x+2 \) represents a downward-opening parabola? This is due to the negative coefficient of the \( x^2 \) term, which gives it a "frown" shape. Among the many properties of parabolas, the vertex represents either a maximum or a minimum point—in this case, it’s the maximum since our parabola opens downward. To find the vertex, you can use the vertex formula \( x = -\frac{b}{2a} \). Plugging in values from our equation where \( a = -3 \) and \( b = 12 \), you'll discover that the x-coordinate of the vertex is at 2. After substituting back into the equation, you can find the maximum y-value to complete your parabolic journey. Happy graphing!

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