Module: Quadratic Equations and Parabolas

I begin by asking the students to consider what happens when we multiply two linear equations together. Start by looking at the graph of (x+1)(x-1). We make a chart of x-values and calculate the values for (x+1),(x-1) and (x+1)(x-1). Then we plot the values for (x,(x+1)(x-1)). The question is, what kind of curve is graphed when the points are connected? What is the y-intercept? How could you find the y-intercept from the two linear factors? What are the x-intercepts? How could you find them from the two linear factors?

Next we actually multiply two linear equations together to see what the product looks like. Multiply (x-2)(x+1). What is this kind of equation called? How is this equation different from a linear equation? What is the degree of this equation? How is it different from a linear equation? Make a chart and pick some x-values and calculate the values for the quadratic equation. Plot the points and sketch the curve. What is the y-intercept? How could you find it from the quadratic equation? What are the x-intercepts? Can you find them from the quadratic equation? What do you need to do to the quadratic equation to find the x-intercepts? Identify the lowest point on the graph as the vertex. What is the x-coordinate of the vertex? From the quadratic equation, how could you find the x-coordinate of the vertex?

Multiply (x+3)(x+2). How did you get the middle term? How did you get the third term? How could you work backwards from the quadratic equation to get the linear factors?

Look at the quadratic equation x²-4. How is this quadratic equation different from the quadratic equations you've seen so far? How could you find the linear factors of this type of quadratic equation?

I finish with some practice on quadratic equations with real solutions. Have them identify the y-intercept and the vertex of the parabola from the quadratic equation, then factor the quadratic equation and find the x-intercepts. Make sure to throw in a difference of two squares quadratic. Give the students a challenging problem like 2x²-3x-2.

The questions in this module are all level 2 and level 3 questions from Costa's Levels of Thinking and Questioning. They require the students to analyze, contrast and compare, generalize, hypothesize and speculate.