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Name: Date: Math 2 Investigation: Finding the Vertex 1. Graph each of these functions on your calculator, and find the vertex using the maximum or minimum command in your calculator. Look for a pattern in the answers. At the end you’ll be asked to identify the pattern. a. f(x) = 2(x – 5)2 + 3. vertex: b. f(x) = –3(x – 4)2 + 5. vertex: (x – 5)2 – 8. vertex: c. f(x) = 1 2 d. f(x) = (x + 1)2 – 6. vertex: f. f(x) = (x – 4)2 – 16. vertex: (you’ll need to adjust the window to see the vertex) Name: Date: Math 2 2. Look for a pattern in the answers to problem 1. Use the pattern to answer these questions. a. Without your calculator, guess the location of the vertex of h(x) = 3(x – 2)2 + 5. Then check it by graphing on your calculator b. At what x value does f (x ) = (x - 2) have its minimum? Explain how you know. 2 c. Fill in the following table. Are the results consistent with your answer to part b? –2 x –1 0 1 2 3 4 g(x) = x 2 f (x ) = (x - 2) 2 d. If the vertex of a parabola is the point (3, 4), then a possible equation for the parabola could be: f (x ) = e. . If the vertex of a parabola is the point (–3, –4), then a possible equation for the parabola could be: f (x ) = f. If the vertex of a parabola is the point (h, k ), then a possible equation for the parabola could be: f (x ) =