QUADRATIC RELATIONS (from y = x2 to y = ax2 + k) Example 1: Sketch each of the following parabolas on the same set of axes: 1 y = x2 y = 2x2 y = x2 y = –x2 2 Complete the following table: Function Vertex Relation to y = x2 (narrower/wider) Direction of Opening Max or Min Value at Vertex y = 2x2 1 2 x 2 y = –x2 y= In general, a VERTICAL STRETCH/COMPRESSION/REFLECTION is given by y = ax2 if a > 1 it is a vertical STRETCH by a factor of a if 0 < a < 1 it is a vertical COMPRESSION by a factor of a if a < 0 it is a REFLECTION in the x-axis Unit 2 Lesson 2 Page 1 of 3 Example 2: Sketch each of the following parabolas on the same set of axes: y = x2 y = x2 + 4 y = x2 – 3 Complete the following table: Function Value of k in y = x2 + k Relation to y = x2 (up/down) Vertex Axis of Symmetry y = x2 + 4 y = x2 – 3 In general, a VERTICAL TRANSLATION is given by y = x2 + k if k > 0 the vertical shift is UP if k < 0 the vertical shift is DOWN Unit 2 Lesson 2 Page 2 of 3 Example 3: Describe the shape and position of each of the following parabolas relative to y = x2: 1 2 a) y = 3x2 + 5 b) y = x –2 4 Example 4: 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 x-axis? a) y = b) y = 1 2 _______________ x – 2 and y = –3x2 + 5 Widest? 2 Farthest? _______________ 1 2 x + 4 and y = 5x2 – 4 3 Widest? _______________ Farthest? _______________ Example 5: Sketch each of the following parabolas on the same set of axes: 1 2 y = x2 y = 2x2 + 3 y= x –2 2 Homework: p.191–192 #4, 7 (don’t graph) Graph: Unit 2 Lesson 2 y = x2 y = x2 – 4 y = –2x2 + 5 1 y = x 2 –2 2 Page 3 of 3

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# QUADRATIC RELATIONS

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