# Activities to Teach Students to Find the Maximum or Minimum Value of a Quadratic Function

As a math student, one of the fundamental skills that you need to master is finding the maximum or minimum value of a quadratic function. Whether you’re studying algebra, geometry, or calculus, this is a skill that you’re going to need at some point or the other. But how do you go about teaching students how to find the maximum or minimum value of a quadratic function? Here are some activities that you can use to make this process more engaging and fun.

This activity is designed to help students understand the concept of maximum and minimum values by using a real-life scenario. The goal of the activity is for students to determine the best price to sell lemonade to maximize profits.

To begin, give your students a scenario where they own a lemonade stand. They must decide the price of the lemonade to maximize their profits. You can set up different scenarios with different amounts of people visiting the lemonade stand, the cost of the ingredients, etc.

After handing out the scenarios, provide some time for students to work in groups or individually to create a graph that will help them analyze the scenarios and make their decisions.

2. The Jellybean Activity

The Jellybean activity is a playful and enjoyable way to introduce students to maximum and minimum values and how to interact with quadratic functions. The activity allows students to make connections between graphs, equations, and data while using technology.

To start, give the student a quadratic function and a graph that represents the function. Then, select an area below the graph and above the x-axis. This area will represent a container containing jellybeans.

Ask the students to create an equation that calculates the volume of the container based on the height of the container, and the maximum number of jellybeans that can fit in the container. From this equation, they can find the maximum value of the container volume.

You could also have the students perform an experiment in the classroom by collecting data on the height of the container and volume of the container to determine the maximum container volume.

3. The Parabola Activity

The Parabola activity is an excellent way to help students understand the relationship between the axis of symmetry of a parabola and its minimum and maximum values. The activity allows the students to use manipulatives to create a parabola and explore its properties.

To start, provide each student with a paper graph with the x-y axis and a set of colored stickies. The stickies should be different colors and different shapes. Tell the students to create a parabola from the stickies. Ask them to determine the axis of symmetry of their created parabola.

Once they’ve placed their stickies, allow the students to color the graph to differentiate between the different stickies. You can also use this activity in combination with algebraic skills so that the students can learn how to calculate the maximum or minimum value of a quadratic function.

Final Thoughts

These activities are fun, engaging, and educational for students of different learning styles. Whenever you are teaching students how to find the maximum or minimum value of a quadratic function, ensure that you provide them sufficient time and different tools to engage with the materials. They’ll have fun and learn a lot. With a little creativity and more imagination, you can come up with many activities to make learning math more enjoyable and memorable for your students.