Problem preview
F-IF.9 Warmup M3-028-A06-V01

Compare functions represented algebraically, graphically, numerically, or verbally.

Compare extrema and turning behavior in parallel

Problem

Compare an upward-opening quadratic with vertex \((3,-2)\), and line \(y=x\).

Big Picture

What this problem is really about

Compare extrema and turning behavior as two related but distinct features. For each graph, identify whether a highest or lowest point exists, then trace the graph from left to right and count actual direction changes. Intersections between the graphs do not count as turns because turning belongs to one function at a time.

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Four variants of this problem type
Curriculum context
Course
Math III
Standard
F-IF.9
Category
Functions
Domain
Interpreting Functions
Objective
Compare functions represented algebraically, graphically, numerically, or verbally.
Problem type
Compare extrema and turning behavior in parallel