Vertex Form and Transformations
I can read the vertex from vertex form and describe the graph as moves of y = x².
What students learn
Students learn to read the vertex (h, k) from y = a(x − h)² + k with the sign of h right, verify it by putting x = h in, and describe the graph as a flip, stretch and moves of y = x².
See inside
The key rule
In y = a(x − h)² + k the vertex is (h, k). A number inside the bracket moves the graph the opposite way to its sign; k moves it as written.
y = a(x − h)² + k
To check a vertex, put x = h in: the bracket is 0, so y comes out as k.
Watch out
A student says y = (x + 4)² − 2 has vertex (4, −2).
The mistake: x + 4, so h = 4The form subtracts h: x + 4 is x − (−4).
The fix: h = −4: vertex (−4, −2)At x = −4 the bracket is 0 and y = −2.
The mistakes it targets
- Reads the sign of h as printed instead of reversing it
- Reverses the sign of k as well as h
- Leaves out the stretch or flip that a causes
- Lets a negative a change the vertex
The interactive Teacher Deck (31 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (three steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: one word problem, a reasoning prompt and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, four common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
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.