Lesson Plan: Finding the Maximum Point of a Parabola

Grade Level: 11th Grade Subject: Algebra 2

Learning Objective: - Students will be able to find the maximum point of a parabola by using the vertex form of a quadratic equation. - Students will understand the relationship between the coefficients of a quadratic equation and the shape of its graph.

DE Standards: - CC.2.3.11.A.1: Understand the relationship between the zeros of a quadratic function and the x-intercepts of its graph. - CC.2.3.11.A.2: Understand the relationship between the vertex of a parabola and the maximum or minimum value of the function it represents.

Materials: - Whiteboard or blackboard - Markers or chalk - Graphing calculators (optional) - Handouts with practice problems

Duration: 1 class period (approximately 45-50 minutes)

Procedure:

1. Introduction (5 minutes):
   • Begin the lesson by asking students to recall what they know about parabolas and their basic shape.
   • Show them a graph of a parabola and ask them to identify any key points or features.
   • Discuss their responses and introduce the concept of the maximum point of a parabola.
2. Activating Strategies (10 minutes):
   • Provide each student with a small whiteboard or a piece of paper.
   • Write a quadratic equation on the board in vertex form, such as y = (x - 2)^2 + 3.
   • Ask students to identify the vertex of the parabola and write it on their whiteboards.
   • Give them a minute to solve it individually, then have them share their answers with a partner.
   • Select a few students to share their answers with the class and discuss the correct solution.
3. Direct Instruction (15 minutes):
   • Explain to students that the vertex form of a quadratic equation is y = a(x - h)^2 + k, where (h, k) represents the vertex.
   • Discuss the role of each coefficient (a, h, and k) in determining the shape and position of the parabola.
   • Emphasize that the value of “a” determines whether the parabola opens upwards or downwards.
   • Demonstrate how to find the maximum point by identifying the vertex coordinates (h, k).
4. Guided Practice (10 minutes):
   • Provide students with handouts containing several quadratic equations in vertex form.
   • In pairs or small groups, have students find the maximum point for each equation.
   • Circulate the classroom to provide assistance and answer any questions.
5. Independent Practice (10 minutes):
   • Assign additional practice problems for students to complete individually.
   • Encourage them to use graphing calculators to verify their answers.
   • Collect their work for assessment purposes.
6. Conclusion (5 minutes):
   • Review the concept of finding the maximum point of a parabola and its significance.
   • Ask students to share any challenges they encountered during the lesson.
   • Summarize the key points and remind students of the importance of understanding parabolas in various applications.

Criteria for Success: - Students correctly identify the vertex of a parabola given its equation in vertex form. - Students accurately find the maximum point of a parabola using the vertex coordinates. - Students demonstrate an understanding of the relationship between the coefficients of a quadratic equation and the shape of its graph.

Note: This lesson plan can be modified to suit the specific needs and time constraints of your classroom.