Question
upstudy study bank question image url

A parabola has a vertex of \( (-4,-1) \) and a y-intercept of 10 . Identify the correct equation of the parabola in vertex form. Select one: \( \begin{array}{l}y=10 / 17(x+1)-4 \\ y=10 / 17(x+4)^{2}-1 \\ y=11 / 16(x+4)^{2}-1 \\ y=10 / 17(x+1)^{2}-4\end{array} \)

Ask by Tucker Weber. in Canada
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The correct equation of the parabola in vertex form is \( y = \frac{11}{16}(x + 4)^2 - 1 \).

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

To find the equation of the parabola in vertex form, we can start with the vertex form of a parabola given by: \[ y = a(x - h)^2 + k \] where \((h, k)\) is the vertex. For this parabola, the vertex is \((-4, -1)\), so we have: \[ y = a(x + 4)^2 - 1 \] Next, we need to find the value of \(a\). We know the y-intercept is 10, which means when \(x = 0\), \(y = 10\). Plugging in the y-intercept: \[ 10 = a(0 + 4)^2 - 1 \] \[ 10 = 16a - 1 \] \[ 11 = 16a \] \[ a = \frac{11}{16} \] Now substituting \(a\) back into the vertex form, we get: \[ y = \frac{11}{16}(x + 4)^2 - 1 \] Thus, the correct equation of the parabola in vertex form is: \[ y = \frac{11}{16}(x + 4)^2 - 1 \] So, the correct answer is \( y=11 / 16(x+4)^{2}-1 \).

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