Linear-Quadratic Systems
I can solve a system of a line and a parabola and give every solution as a point.
What students learn
Students learn to solve a system of a line and a parabola: they set the two rules for y equal, solve the quadratic, give each x its own y, and say whether there are two, one or no solutions.
See inside
The key rule
Set the right sides equal and solve the quadratic: two, one or no solutions. Give each x its own y.
ax² + bx + c = mx + k
Write the quadratic = 0 to solve it. Answer with points, and check every point in both equations.
Watch out
A student solves y = x² and y = x + 6 and answers (3, 9).
The mistake: (3, 9)One point; x = −2 was dropped.
The fix: (3, 9) and (−2, 4)x = −2 gives y = −2 + 6 = 4.
The mistakes it targets
- Stops at one intersection point
- Gives only the x-values
- Writes the y-coordinate first
- Reads a discriminant of 0 as no solution
- Moves a constant across the equal sign without changing its sign
- Gives both x-values the same y-value
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, six 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.