math class 678 4-in-1 skill sheets
Vertex Form and Transformations, Algebra 1 4-in-1 Skill Sheet (HSF.BF.B.3)
HSF.BF.B.3 Algebra 1 Unit 12: Quadratic Functions

Vertex Form and Transformations

I can read the vertex from vertex form and describe the graph as a transformation of y = x squared.

View on TPT Back to Unit 12

The problem this sheet solves

Vertex form SUBTRACTS h, so the graph of (x minus 3) squared moves RIGHT — the opposite of what the symbol suggests. And k does not reverse, because it sits outside the bracket, so students who over-apply the reversal flip both and land back where they started. This is the same fact in a third costume — point-slope form had the subtraction built in, and function transformations reverse inside the bracket — so the sheet names it as a known pattern rather than teaching it again from scratch: anything INSIDE the bracket acts on the input and runs backwards. The check is one substitution: put h in and the bracket vanishes, so y = k and that IS the vertex. Every item has a non-zero k on purpose.

The key rule

In y = a(x − h)² + k the vertex is (h, k). The bracket SUBTRACTS h, so the sign you see is not the sign of the answer.

Inside reverses. Outside does not.

Watch out

The mistake: A student says y = (x − 3)2 + 2 has vertex (−3, 2).

The fix: (3, 2). The form subtracts h, so the minus you can see IS the subtraction. Substituting x = 3 makes the bracket zero and leaves y = 2; x = −3 gives 38.

What is included

  • Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
  • Practice page — six problems, building from foundational to multi-step
  • Apply page — a word problem, a reasoning prompt, and an error-analysis task
  • Assess — a half-page exit ticket, two to a sheet, with a score box
  • Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
  • Ink-saver edition of all 7 pages
  • 14-slide teacher deck (PowerPoint) with presenter notes on every slide

Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.