Original Expression: x² // Given expression
Transformation: Shift by 1 downward:
a. x² – 1 // Shifting the graph of x² one unit downward
Action on Specific Points:
b. Action on (-1,1): (-1,1) becomes (-1,0) // Shifting the point one unit downward
c. Action on (0,0): (0,0) becomes (0,-1) // Shifting the point one unit downward
d. Action on (1,1): (1,1) becomes (1,0) // Shifting the point one unit downward
Graphing the Entire Curve:
e. Take several points on the original curve x² and shift each one unit downward
f. Plot the shifted points on a coordinate plane
g. Draw a smooth curve through the shifted points to represent the graph of x² – 1
h. Note: The vertex of the parabola shifts from (0,0) to (0,-1), and the parabola opens upward
Final Expression: x² – 1 // Final result
Original Expression: x² // Given expression
Transformation: Shift by 1 downward:
a. x² – 1 // Shifting the graph of x² one unit downward
Action on Specific Points:
b. Action on (-1,1): (-1,1) becomes (-1,0) // Shifting the point one unit downward
c. Action on (0,0): (0,0) becomes (0,-1) // Shifting the point one unit downward
d. Action on (1,1): (1,1) becomes (1,0) // Shifting the point one unit downward
Graphing the Entire Curve:
e. Take several points on the original curve x² and shift each one unit downward
f. Plot the shifted points on a coordinate plane
g. Draw a smooth curve through the shifted points to represent the graph of x² – 1
h. Note: The vertex of the parabola shifts from (0,0) to (0,-1), and the parabola opens upward
Final Expression: x² – 1 // Final result
Original Expression: x² // Given expression
Transformation: Shift by 1 upward:
a. x² + 1 // Shifting the graph of x² one unit upward
Action on Specific Points:
b. Action on (-1,1): (-1,1) becomes (-1,2) // Shifting the point one unit upward
c. Action on (0,0): (0,0) becomes (0,1) // Shifting the point one unit upward
d. Action on (1,1): (1,1) becomes (1,2) // Shifting the point one unit upward
Graphing the Entire Curve:
e. Take several points on the original curve x² and shift each one unit upward
f. Plot the shifted points on a coordinate plane
g. Draw a smooth curve through the shifted points to represent the graph of x² + 1
h. Note: The vertex of the parabola shifts from (0,0) to (0,1), and the parabola opens upward
Final Expression: x² + 1 // Final result