A.6.12.2 Quadratic Graphs Galore
Using graphing technology, graph y = x2, and then experiment with each of the following changes to the function. Record your observations (include sketches, if helpful).
1. Adding different constant terms to x2 (for example: x2 + 5, x2 + 10, x2 - 3, etc.)
2. Multiplying x2 by different positive coefficients greater than 1 (for example: 3x2, 7.5x2, etc.)
Multiplying x2 by different negative coefficients less than or equal to -1 (for example: -x2, -4x2, etc.)
4. Multiplying x2 by different coefficients between -1 and 1 (for example: 1/2x2, -0.25x2, etc.)
The points (1, 1), (2, 4) and (3, 9) are three points on the graph representing x2. When we add 3 to x2 how do the values for x=1, x = 2, and x = 3 change? What about when we subtract 3 from x2?
How do the values change when you multiply x2 by a positive number, say, 3?
How do the tripled values affect the graph?