Unit 8: Linear & Quadratic Systems and Inequalities (Math 20-1)
Linear–quadratic & quadratic–quadratic systems; inequalities in one/two variables (with & without technology).
Solve by Substitution
Discriminant & Intersections
Sign Charts
Half-planes & Regions
Modelling
What You Should Be Able To Do
- Solve linear–quadratic systems (e.g., \(y=ax^2+bx+c\) & \(y=mx+k\)); classify # of intersections via \(\Delta\).
- Solve quadratic–quadratic systems by equating and solving a quadratic in \(x\).
- Solve linear and quadratic inequalities in one variable using algebra and sign charts; write solutions in interval notation.
- Graph and interpret inequalities in two variables (lines/parabolas): boundary type, region, intercepts, and context.
Progress autosaves to this device.
Video Library
Linear–Quadratic Systems
Substitution, # of solutions via discriminant.
youtube.com – “linear quadratic system solve substitution”Quadratic–Quadratic Systems
Equate and solve resulting quadratic.
youtube.com – “solve quadratic quadratic systems”Quadratic Inequalities & Sign Charts
Intervals, open/closed endpoints.
youtube.com – “quadratic inequalities sign chart”Graphing Inequalities in 2 Variables
Boundary, shading, intercepts & context.
youtube.com – “graphing inequalities two variables parabola line”Interactive Tools
Systems Explorer (L–Q and Q–Q)
Inequalities in One Variable
Graph Linear Inequality \(ax+by\ \rel\ c\)
Graph Parabolic Inequality \(y\ \rel\ ax^2+bx+c\)
Unit 8 Quizzes
Downloadable Review
Quick Practice Scratchpad
Try: solve \(y=x^2-4\) and \(y=2x+1\); solve \(x^2-5x+6\le0\); graph \(2x+3y\ge12\); shade \(y\le -x^2+4\).