Exploring Roots of a Quadratic Equation, Page 3

 Did you get 2 and -3? The parabola crosses the x-axis at (2, 0) and also at (-3, 0). Let's think about those two numbers: The sum of 2 and -3 is -1. The product of 2 and -3 is -6. 2 and -3 are the roots of the quadratic equation. The roots satisfy the equation: ``` y = x^2 + x - 6 y = (x - 2)(x + 3) y = x - 2 or y = x + 3 If y is 0, then 0 = x - 2 or 0 = x + 3 x = 2 or x = -3 CHECK: 0 = 2^2 + 2 - 6 or 0 = (-3)^2 + (-3) - 6 0 = 4 + 2 - 6 or 0 = 9 - 3 - 6 0 = 6 - 6 or 0 = 9 - 9 0 = 0 or 0 = 0 ``` Here's another parabola to graph. Select 0 for a and -4 for b on the blue graph. In other words, click on the point (0, -4) on the blue graph. Now think about what two numbers have sum 0 and product -4? Can you name those two numbers by noting where the parabola crosses the x axis on the green graph? What is the quadratic equation? What is that equation in factored form? What are the roots of the equation? CHALLENGE: Can you find another parabola and identify the roots? Final Task Think about the following: How do a and b affect the location of the parabola? How can you know the quadratic equation by looking at the green graph? Generalize how the applet can be used to find the roots of a quadratic equation. Page 1 || Page 2 || Page 3

 Math Forum Resources Analytic Geometry Formulas Analytic geometry (a branch of geometry in which points are represented with respect to a coordinate system, such as cartesian coordinates) formulas for figures in one, two, and three dimensions: points, directions, lines, triangles, polygons, conic sections, general quadratic equations, spheres, etc. Describing the Graph of an Equation Which of the following is true of the graph of the equation: y = 2x^2 - 5x + 3? Equations and Factoring Solve. Identify all double roots: 2(r^2 + 1)=5r Graphing Parabolas How do you know how to graph a parabola from looking at its equation? Learning to Factor A sampling of answers from our archives. What is a Quadratic Equation? What is a quadratic equation? What is it used for? How can we use it to solve everyday problems?