Solving Quadratics by Square Roots
I can solve x² = k and (x − h)² = k by taking both square roots.
What students learn
Students learn to solve x² = k and (x − h)² = k: they get the square alone, take both square roots, finish solving for x, give exact answers in simplest radical form, and say when there is no real solution.
See inside
The key rule
Get x² by itself first. If k > 0, x² = k gives x = ±√k: two solutions. k = 0 gives one; k < 0 gives none.
x² = k, k ≥ 0 → x = ±√k
(x − h)² = k with k ≥ 0: x − h = ±√k, so x = h ± √k.
Watch out
A student solves x² = 49 and writes x = 7.
The mistake: x = 7That is only the positive root.
The fix: x = 7 or x = −7(−7)² = 49 too: squaring hides the sign.
The mistakes it targets
- Takes only the positive square root
- Halves the number instead of taking its square root
- Undoes an added constant by adding
- Stops before solving for x after taking the root
- Gives real answers when the square equals a negative number
- Multiplies instead of dividing to get x² alone
The interactive Teacher Deck (32 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 (four 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, seven 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.