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Quadratic Equations: Warm-Up Exercises and Graphing Techniques for 6th Grade Math

This warm-up sheet focuses on reviewing key concepts related to quadratic equations and their characteristics. Students are encouraged to recall the standard form of a quadratic equation and the formula for finding the x-coordinate of the vertex of a parabola. The lesson includes transformations of the parabola, specifically the vertex form, and provides examples to illustrate graphing from vertex form. Students will identify constants, plot the vertex, and show the axis of symmetry. An assignment follows to reinforce these concepts.

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Quadratic Equations: Warm-Up Exercises and Graphing Techniques for 6th Grade Math

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  1. Acc Math 1 Dec. 6th • WARM-UP • No new warm-up sheet. Just do these on a piece of notebook paper. • Look at your notes from yesterday: • What is the standard form of quadratic equations? • What formula do you use to find the x coordinate for the vertex of the parabola?

  2. Characteristics of Quadratics f(x) = x2 Standard Form: f(x) = ax2 + bx + c Transformations: f(x) = a(x – h)2 + k (vertex form) a – h – k –

  3. Example Example f(x) = 2x2 – 4x – 6 f(x) = 3x2 – 6x + 1 Vertex: Axis of sym: 2 other points:

  4. GRAPHING FROM VERTEX FORM Example 1: Graph y = ½(x + 1)2 – 2 • IDENTIFY the constants. a = _____, h = _____, k = ____ • Because a ____ 0, the parabola opens ________. • Plot the vertex (h, k) = (____, ____) and draw the axis of symmetry at x = ____ • Plot the points (___, ___) and (___, ___) and their reflections

  5. Example Example f(x) = 2(x + 5)2 – 4 f(x) = - ½ (x – 3)2 + 1 Vertex: Axis of sym: 2 other points:

  6. ASSIGNMENT • Pages 5-6 PROBLEMS -19

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