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Unformatted text preview: 14 Quadratic Functions and Their Graphs
Sketching the graph of a parabola: f(x) = ax2 + bx + c
1. if a > 0, it opens up
if a < 0, it opens down − b − b , f this is a key point!
2. plot vertex: 2a 2a 3. plot xintercepts: solve f(x) = 0 to get them
4. plot yintercept: f(0) = c, so yintercept = c
5. plot more points on either side of the vertex as
necessary to round out picture
Example: f(x) = x2 + 2x + 3 (a = 1, b = 2, c = 3) 1. a < 0 so
2. = =
f() = , so
3. solve x2 + 2x + 3 = 0:
(x + 3)(x + 1) = 0
x = 3, 1
4. c = 3, so
5. f(2) = 3 opens down 14 vertex: (1,4)
xintercepts: (3, 0), (1, 0)
yintercept: (0, 3)
additional point: (2,3) p. 1 ...
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.
 Spring '11
 Staff

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