# POLQ 3 | Lesson 1 | Explore (Multiplying two Linear Functions)

Did you find that the first line had the equation:  $$y = \frac{1}{2}(x+3)$$?

2. Graph a second line, $$y = 2x – 4$$,  on the same coordinate plane, and write the equation for this line in $$y = m(x + c)$$ form.

3. What is “$$c$$”? Is it something observable on the graph of each line?

4. Create a $$t$$-table with y values for the same $$x$$-values from each line. Take the product of the two $$y$$-values and graph for each $$x$$-value. What type of graph does it appear to make?

5. Now multiply the two linear expressions from questions #1 and #2 and graph the resulting parabola. How does the graph of the equations compare to the graph of the parabola in #4.

6. Compare and contrast the graph of the parabola to the graphs of the lines. Write down as many similarities as you can find? Make notes regarding features of the parabola such as the coordinate of the vertex and where the y-values are negative both on the parabola and on the lines.

Example