Interpret key graph/table features of quadratic models in context.
Identify where a quadratic model is increasing and decreasing from vertex form
Problem
Analyze where \(f(x)=(x-3)^{2}+1\) decreases and increases. Identify the vertex input and opening direction, then state both open intervals and explain the behavior change at \(x=3\).
Big Picture
What this problem is really about
A quadratic changes direction at the vertex input, while its opening tells which behavior occurs on each side. We’ll track how distance from the vertex changes as x moves left to right, assign the corresponding decrease and increase, and state the behavior on open intervals that exclude the turning input.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
