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QUADRATIC RELATIONS (An Introduction) Example The graph shows a soccer ball’s height above the ground over time after it was kicked in the air. a) Describe the shape of the graph. b) What was the ball’s maximum height? c) How long was the ball in the air? vertex: is the point at which the graph changes from decreasing to increasing or from increasing to decreasing A parabola always has a minimum or maximum value (the y-coordinate of the vertex). CASE If the parabola opens up there will be a minimum value. Unit 2 Lesson 1 CASE If the parabola opens down there will be a maximum value. Page 1 of 3 Example The table shows how two variables, x and y, are related. x y 0 1 2 3 4 5 6 1 6 9 10 9 6 1 First Differences a) Calculate the first and second differences. b) Is the relation linear or quadratic? degree: Second Differences _________________________ the degree of a polynomial with a single variable is the value of the highest exponent of the variable Example Which of the relations are quadratic? a) y = 4x – 5 Degree? _____ b) y = 2x2 + 5x – 8 Degree? _____ SUMMARY To identify a quadratic function: Quadratic Functions Table of Values Graph Equation Unit 2 Lesson 1 Page 2 of 3 THE BASIC PARABOLA Sketch the graph of y = x2 using the given table of values: x -3 -2 -1 0 1 2 3 y ordinate differences: the differences in the y-coordinates V(0,0) OD: 1, 3, 5, … y x Homework: p.174–175 #1abe, 2, 3a, 4 Unit 2 Lesson 1 Page 3 of 3