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QUADRATIC RELATIONS (from y = x2 to y = a(x – h)2) Example 1: Sketch each of the following parabolas on the same set of axes: y = x2 y = (x – 2)2 y = (x + 3)2 Complete the following table: Function Value of h in y = (x – h)2 Relation to y = x2 (left/right) Vertex Axis of Symmetry y = (x – 2)2 y = (x + 3)2 In general, a HORIZONTAL TRANSLATION is given by y = (x – h)2 if h > 0 the horizontal shift is RIGHT if h < 0 the horizontal shift is LEFT Example 2: Suppose each pair of relations were graphed on the same set of axes. Which parabola would be the widest (most vertically compressed)? Which parabola would have its vertex farther from the y-axis? a) y = 1 ( x 3)2 and y = –5(x + 4)2 2 b) y = 2(x + 3)2 and y = 3(x – 2)2 Widest? _____________ Farthest? _____________ Widest? _____________ Farthest? _____________ Unit 2 Lesson3 Page 1 of 2 Example 3: Sketch each of the following parabolas on the same set of axes: y = x2 Example 4: y = –2(x + 4)2 y= 1 ( x 3)2 2 Describe the shape and position of each of the following parabolas relative to y = x2: 1 a) y = –2(x + 1)2 b) y = ( x 2)2 3 Homework: p.200–201 #2 (don’t graph), 5 Graph: Unit 2 Lesson3 y = x2 y = –(x + 5)2 y = 3(x – 1)2 1 y = ( x 2)2 2 Page 2 of 2