# Lines - Multiplying

## What does it mean to Multiply Functions (Lines)?

This activity continues the idea introduced in the Lines - Adding Activity where we build on and extend concepts related to comparisons (=, >, <) and operations (+, -, * , ÷) with numbers in elementary grades to comparisons (=, >, <) and operations (+, -, * , ÷) with functions in subsequent grades. A function-based approach to algebra supports very general approaches to understanding key mathematical ideas that will support student advancement through high school and beyond. For this activity we can ask in what ways is multiply a linear function by another linear function analogous to multiplying 3 * 2? Activities extending this introduction are included below.
Explore what the environment does. What do you notice? How many different kinds of parabolas can you make from multiplying lines. Use the vertical dotted line slider to explore how the multiplication works. How can we explain when the parabola is above and below the x-axis. Why does the parabola and the lines cross the x-axis at the same point. Then, use the following environment (or graphing calculators) to Find TWO PAIRS of lines in slope-intercept form that when multiplied each pair gives a concave downward parabola that intersects the x-axis in two locations. Then write each resultant parabola in standard form (e.g., Y4 = ax^2 + bx + c). Find TWO PAIRS of lines in slope-intercept form that when multiplied each pair gives a concave upward parabola that intersects the x-axis in two locations. Then write each resultant parabola in standard form (e.g., Y4 = ax^2 + bx + c).