Graphing Quadratics in Standard Form
I can graph a quadratic from standard form by finding the axis of symmetry and the vertex first.
The problem this sheet solves
The minus in the vertex formula gets dropped because b already carries a sign, and the result is not merely a different number. It relocates the whole graph. Students taught to plot five points and join them cannot catch it either, since their curve's lowest drawn point is wherever the table happened to land. This sheet installs a self-check that needs no formula: a parabola is symmetric, so the vertex sits exactly halfway between the x-intercepts. For this one they are 1 and 5, and minus 3 is not between them. Every item has rational intercepts so the check is always available. The order taught is axis first, then vertex, then a point either side USING the symmetry.
The key rule
Find x = −b/(2a) first, substitute it for the vertex, then use symmetry for the rest. The sign of a says which way it opens.
Axis, vertex, then mirror.
Watch out
The mistake: A student says the axis of symmetry of y = x2 − 6x + 5 is x = −3.
The fix: x = 3. b is already −6, so −b is +6. The intercepts are 1 and 5, and the vertex must sit halfway between them.
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.