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Algebra 2 Notes – Lesson 5.3 [Type text] f ( x) x 2 The “Parent” Function of the Quadratic: 5 We can transform the quadratic the same way we did with the absolute value function. 4 3 2 1 “VERTEX FORM”: f(x) = a(x –h)2 + k -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 a, h, and k do the same things as before -4 -5 Notice how the graph increases. Up 1 over 1. Up 3 over 1. Up 5 over 1. Describe, in order, the sequence of transformations of each function and then graph the function by hand. 2 1) f ( x) 2 x 4 2) f ( x) 1 x 2 2 5 3) f ( x) 1 x 12 2 3 2 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 -1 -1 -1 -2 -2 -2 -3 -3 -3 -4 -4 -4 -5 -5 -5 2 3 4 5 Algebra 2 Notes – Lesson 5.3 [Type text] Write a function for the graph below. 1. How is the graph translated? __________________ 8 6 4 2. Use the translation to write an equation: __________________ 2 -8 -6 -4 -2 2 4 6 8 -2 3. Find a value for a: -4 -6 -8 Write a function for the graph below. 1. How is the graph translated? __________________ 8 6 4 2. Use the translation to write an equation: __________________ 3. Find a value for a: 2 -8 -6 -4 -2 2 -2 -4 -6 -8 4 6 8 Algebra 2 Notes – Lesson 5.3 [Type text] Write a function for the graph below. 1. How is the graph translated? __________________ 8 6 4 2. Use the translation to write an equation: __________________ 3. Find a value for a: 2 -8 -6 -4 -2 2 -2 -4 -6 -8 4 6 8