The Quadratic Formula
I can solve any quadratic with the quadratic formula, dividing the whole numerator by 2a.
The problem this sheet solves
This is a GROUPING error, not a formula error, and correcting it as though the formula were wrong misses it entirely. A printed fraction bar is a grouping symbol that does a bracket's job, and the bar disappears the moment the formula is written on one line — which is exactly what a calculator forces. The reference figure writes the formula FLAT with the bracket put back, and the anatomy row sets both groupings beside their answers so the difference is a number rather than a warning. The fastest correction is a substitution the student does themselves. One item is deliberately the previous sheet's equation, so the same answers arrive by a second route and the formula is seen as completing the square done once in general.
The key rule
x = (−b ± √(b2 − 4ac)) ÷ 2a. The whole numerator goes over 2a, not just the radical.
The bar is a bracket.
Watch out
The mistake: A student computes −5 ± 7 ÷ 4 and answers −13/4 and −27/4.
The fix: The bar covers the whole top. It is (−5 ± 7) ÷ 4, giving 1/2 and −3. Substitute their values: neither one works.
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.