Back to Compare function properties — Problem 5 · Task Set 27

HSF.IF.C.9 Tutor Intake — Comparing Properties Across Representations

This short check helps your tutor understand where to start. Answer each question on your own. If you are not sure, give your best try — every response helps your tutor plan your sessions.

Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-if-c-9

Work through problems with immediate feedback

Procedures

Function A (algebraic): $f(x) = -x^2 + 6x - 5$

Function B (graph): a downward-opening parabola with vertex at
approximately $(1, 4)$ .

A student completes the square on Function A and finds that its
maximum is exactly 4, occurring at $x = 3$ . Based on this and the
graph description, which statement is best supported?

Function A has a larger maximum because algebra gives exact values while the graph is an estimate.

Function B has a larger maximum because its vertex appears to be at 4 from the graph.

Both functions appear to have a maximum of 4; Function A''s maximum
is confirmed exactly as 4, while Function B''s maximum is estimated
as approximately 4 from the graph.

Function B has a larger maximum because graphical methods are more reliable than algebra.