Algebra 1 | Unit 6 | Lesson 3: Building Quadratic Functions from Geometric Patterns | Practice Problems

Here are a few pairs of positive numbers whose difference is 5. Find the product of each pair of numbers. Then, plot some points to show the relationship between the first number and the product. Is the relationship between the first number and the product exponential? Explain how you know.

Here are some lengths and widths of a rectangle whose perimeter is 20 meters. Complete the table. What do you notice about the areas? Without calculating, predict whether the area of the rectangle will be greater or less than 25 square meters if the length is 5.25 meters. On the coordinate plane, plot the points for length and area from your table. Do the values change in a linear way? Do they change in an exponential way?