Mathematics > GIZMOS > Roots of a Quadratic Gizmo | All Answers Correct (All)

Roots of a Quadratic Gizmo | All Answers Correct

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Student Exploration: Roots of a Quadratic Vocabulary: axis of symmetry, complex number, conjugates, discriminant, imaginary number, parabola, quadratic equation, quadratic formula, quadratic functio ... n, root of an equation Prior Knowledge Questions (Do these BEFORE using the Gizmo.) 1. Factor x 2 + 3x + 2 by filling in the blanks: x 2 + 3x + 2 = (x + )(x + ) (Hint: The numbers in the blanks have a sum of 3 and a product of 2.) 2. What two values of x make the product above equal to zero? 3. Plug each of these values into x 2 + 3x + 2. What do you get? Gizmo Warm-up Quadratic functions are functions of the form f(x) = ax2 + bx + c. The graph of a quadratic function is a parabola, as shown to the right. When working with quadratic functions, it is often useful to find the values of x that make f(x) equal to zero. Factoring is one way to find these values, but factoring is not always easy. In the Roots of a Quadratic Gizmo, you will use algebraic and graphical methods to explore the values of x that make f(x) = 0. To begin, graph y = x 2 + 3x + 2 by setting a to 1.0, b to 3.0, and c to 2.0. (Change the values by dragging the sliders, or by clicking in the text field, typing in a value, and hitting Enter.) 1. The blue points are x-intercepts of the parabola. They are the points where y = 0. Mouseover the blue points. What is the x-coordinate of each point? 2. The x-intercepts are solutions, or real roots, of the quadratic equation x 2 + 3x + 2 = 0. A. Plug each solution into x 2 + 3x + 2. What do you get? B. Recall that x 2 + 3x + 2 = (x + 1)(x + 2). How do these factors relate to the x-intercepts of y = x 2 + 3x + 2 [Show More]

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