Algebra I Lesson

Roots Revealed: Graphing Square Root & Cube Root Transformations

Shared by A STEM Educator

8th or 9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.HSF.IF.C.7b, CCSS.MATH.CONTENT.HSF.BF.B.360 min

Learning Objective

Students will graph square root and cube root functions in the form $y = a x - h + k$ and $y = a 3 x - h + k$ , identify the endpoint or inflection center $(h, k)$ , state domain and range, and determine the value of $a$ given a point on the curve.

Lesson Overview

Students move from noticing domain differences between square and cube root tables, through progressive graphing of transformations, to writing equations from geometric clues — all at vertical whiteboards in random groups.

Materials

Vertical non-permanent surfaces (whiteboards or chart paper on walls)
Dry-erase markers (one per group)
Random grouping cards or app
Anchor chart paper for consolidation
Individual mini-whiteboards or paper for exit slip
Desmos Classroom activity (teacher-created, see Part 3 spec)

Scaffolded Task Progression

1Task 1

Low-Floor Launch (verbal delivery): Graph the parent curve

y = x

on your board using integer outputs at

x = 0, 1, 4, 9

. State the domain and range. Now, on the same grid, plot

y = x + 3

and

y = x - 4

. Describe how adding

3

outside versus subtracting

4

inside shifts the starting endpoint

(0, 0)

of the parent curve.

2Task 2

Slice 1 — The Endpoint Shift Rule: Predict the starting endpoint, domain, and range of

y = x + 5 - 2

without making a full table. Sketch the curve on your board and verify using three strategic

x

-points.

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