Lesson Plan

• Describe how the shape of a quadratic graph determines the sign of the expression.
• Apply both graphical and algebraic methods to solve quadratic inequalities.
• Construct and interpret sign‑charts to identify solution intervals.
• Write solution sets correctly using inequality and interval notation.
• Identify common errors and avoid them when solving quadratic inequalities.

• Projector/interactive whiteboard
• Graph paper, rulers, and pencils
• Worksheet with practice quadratic inequalities
• Scientific calculators or algebra software
• Whiteboard and markers
• Pre‑printed sign‑chart templates

Begin with a quick “What’s the shape of y = x²?” poll to activate prior knowledge of parabolas. Review how the leading coefficient determines opening direction and how roots split the x‑axis. Explain that today’s success criteria are to solve a quadratic inequality correctly and to express the answer in proper notation.

1. Do‑Now (5'): Students complete a short worksheet identifying the roots of a given quadratic and sketching its graph.
2. Mini‑lecture (10'): Review graphical method steps; demonstrate with y = x²‑5x+6 on the board.
3. Guided Graphing Activity (15'): In pairs, students draw the parabola for a new inequality, locate intercepts, and write the solution set.
4. Algebraic Method Demonstration (10'): Show how to form the sign chart, compute the discriminant, and determine sign patterns.
5. Sign‑Chart Practice (15'): Students complete a sign‑chart template for a given inequality, then compare answers.
6. Independent Practice (10'): Worksheet with four mixed inequalities (graphical or algebraic).
7. Exit Ticket (5'): Write one correct solution set for a quadratic inequality and note one common mistake to avoid.

Recap the two solution pathways and emphasise the importance of checking the sign of the leading coefficient. Collect exit tickets to gauge understanding, and assign homework: three additional quadratic inequalities to solve using either method.