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QUADRATIC RELATIONS (from y = x2 to y = a(x – h)2 + k) SUMMARY: y = a(x – h)2 + k vertical stretch (a > 1) vertical compression (0 < a < 1) reflection (x-axis) (a = –1) Example 1: horizontal translation (+) move left (–) move right vertical translation (+) move up (–) move down Consider the given parabola: a) Identify the coordinates of the vertex. b) State the values of h and k. h= k= c) Is the value of a positive or negative? d) Determine the value of a. a= e) Write an equation for the parabola in the form y = a(x – h)2 + k. Example 2: The parabola y = x2 is transformed. Write the equation of each transformed parabola in the form y = a(x h)2 + k. a) vertically stretched by a factor of 3, reflected in the x-axis, and translated 5 units left and 1 unit down; _________________ b) vertically compressed by a factor of ½ and translated 3 units right and 5 units up. Unit 2 Lesson4 _________________ Page 1 of 2 Example 3: Complete the following table: Function Vertex Axis of Relation to y = x2 Symmetry (narrower/wider) Direction of Opening Max or Min Value 1 y = (x – 4)2 + 3 2 y = –3(x + 5)2 – 2 Example 4: Sketch each of the following parabolas on the same set of axes: 1 y = x2 y = (x – 4)2 + 3 y = –3(x + 5)2 – 2 2 Homework: p.212–214 #1abfh, 2cegh, 4acd Unit 2 Lesson4 Page 2 of 2