Lesson Plan

• Describe how the vertex provides the maximum or minimum value of a quadratic function.
• Apply completing the square to find the vertex of any quadratic in standard form.
• Sketch the graph of a quadratic using the vertex, intercepts and the direction of opening.
• Determine the range of a quadratic when the domain is restricted to a specific interval.
• Solve practice problems accurately and verify results using the vertex method.

• Projector or interactive whiteboard
• Printed worksheet with example questions
• Graph paper and rulers
• Calculator or graphing app
• Whiteboard markers
• Set of quadratic‑function cards (optional)

Begin with the question, “How can we draw a parabola in seconds?” Connect to prior knowledge of standard form and intercepts. Explain that today’s success criteria are to locate the vertex, sketch the curve quickly, and state the range for a restricted domain.

1. Do‑now (5'): Students write the vertex formula $h=-\frac{b}{2a},\;k=c-\frac{b^{2}}{4a}$ from memory.
2. Mini‑lecture (10'): Demonstrate completing the square and derive the vertex form.
3. Guided practice (12'): Work through Example 1 together – find vertex, intercepts, and sketch the graph.
4. Pair activity (10'): Each pair sketches a new quadratic and determines its range for a given domain using the step‑by‑step procedure.
5. Whole‑class review (8'): Share sketches, discuss common errors, and answer questions.
6. Exit ticket (5'): Write the vertex and the range for a supplied quadratic on a slip of paper.

Recap the link between the vertex and both graphing and range determination. Collect exit tickets to gauge understanding, and assign homework to convert three quadratics to vertex form and sketch them.