Transforming Quadratic Functions Lesson Plan for 9th Grade Students

Topic: Transforming quadratic functions

Objectives & Outcomes

• Students will be able to understand how the parabola shift (up, down, right and left) and how it stretch.

Materials

• Graph paper
• Pencils
• Calculator (optional)

Warm-up

• Begin the lesson by asking the students to recall what a parabola is. Ask them to describe its shape and how it differs from a circle or a straight line.
• Next, write the equation of a parabola, y = a(x - h)2 + k, on the board and ask the students to explain what each part of the equation means.
• Ask the students to consider the following question: can we change the position of the parabola (up, down, right or left) without changing its shape?

Direct Instruction

• Explain to the students that by manipulating the coefficients of the parabola equation, we can move the parabola up, down, right or left without changing its shape.
• For example, if we replace the coefficient a with -a, the parabola will be shifted down by a unit. If we replace the coefficient a with a2, the parabola will be shifted up by a unit.
• Next, explain to the students that by manipulating the coefficient k, we can stretch or shrink the parabola. If we replace the coefficient k with k - 1, the parabola will be stretched by a factor of 1/k. If we replace the coefficient k with k + 1, the parabola will be shrunk by a factor of 1/k.
• Demonstrate these transformations on a graph and have the students observe the changes.

Guided Practice

• Have the students work in pairs and give each pair a parabola equation with manipulated coefficients.
• Have the students manipulate the coefficients and explain their reasoning.
• Have the students use a calculator to graph the parabola and compare it to the original graph.

Independent Practice

• Provide students with a worksheet that has several different parabola equations.
• Have the students identify the manipulation that was made to the coefficients, and graph each parabola.
• Have the students discuss the differences in the parabola shapes and how they are affected by the manipulation.

Closure

• Review the concept of parabola transformations and how they affect the shape of the parabola.
• Ask students to share any questions or concerns they have about the topic.

Assessment:

• Observe students during the guided and independent practice to assess their understanding of the material.
• Collect and grade the completed worksheets and projects.