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:

- 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.

- 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.

- 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).

- 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.

- 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.

- 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.

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