Key Features of Parabolas
I can name a parabola's vertex, axis of symmetry, intercepts, domain, range and intervals.
What students learn
Students learn to give the vertex and its maximum or minimum value, the axis of symmetry as an equation, the intercepts as points, the domain and range, and where a parabola increases and decreases.
See inside
The key rule
The domain of y = ax² + bx + c is all real numbers (unless a context limits it). The range starts at the vertex's y and runs one way: y ≥ k when it opens upward, y ≤ k when it opens downward.
vertex (h, k): axis x = h
Increasing and decreasing use <; the range uses ≥ or ≤, because k itself is an output.
Watch out
A student says y = x² − 8x + 10 has domain and range all real numbers.
The mistake: range: all real numbersIt turns at (4, −6): no output is below −6.
The fix: domain: all real numbers; range: y ≥ −6The domain half was right; the range starts at the vertex.
The mistakes it targets
- Gives the range of a parabola as all real numbers
- Gives where the minimum or maximum occurs as its value
- Runs the range the wrong way from the vertex
- Writes the axis of symmetry as a number instead of an equation
- Reads an interval past the vertex or from right to left
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, five 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.