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Transformation of Quadratic Functions - Group 4 - Coggle Diagram
Transformation of Quadratic Functions - Group 4
Vertical
The graph shifts upward or downward
When the coordinates of a graph are originally (0,0) and shift to (0, 8), the graph is said to have shifted up by 8 units
When the coordinates of a graph are originally (0,0) and shift to (0, 8), the graph is said to have shifted up by 8 units
Horizontal
The graph moves to the right or left
When the coordinates of a graph are originally (0,0) and shift to (4, 0), the graph is said to have shifted to the right by 4 units
When the coordinates of a graph are originally (0,0) and shift to (4, 0), the graph is said to have shifted to the left by 4 units
Formula:
y = (x - h)^2 + k
Horizontal
If h is negative, the formula is y = (x + h)^2 + k which means the slope shifts to the left by h units
If h is positive, the formula is y = (x - h)^2 + k which means the graph shifts to the right by h units
Vertical
If k is negative, the formula is y = (x - h)^2 - k which means the slop shifts down by k units
If k is positive, the formula is y = (x - h)^2 + k which means the slope shifts up by k units
Reflection on x axis: The formula is y = -(x - h)^2 + k as the y coordinate changes to become negative/positive on the graph and the x coordinate remains the same
Reflection on y axis: The formula is y = (-x - h)^2 + k as the x coordinate changes to become negative/positive on the graph and the y coordinate remains the same
Reflection
On x axis
When the slope is reflected on the x axis, only the y coordinate will change and become negative or positive depending on its original value.
Eg: a graph with the coordinates (2, 3) will be reflected on the x axis to give the coordinates (2, -3)
On y axis
When the slope is reflected on the y axis , only the x coordinate will change and become negative or positive depending on its original value.
Eg: a graph with the coordinates (2, 3) will be reflected on the y axis to give the coordinates (-2, 3)
Dilation:
Horizontal
Represented by b in the formula a(bx - h)^2 + k
There is a stretch when the value of b is between 0 and 1.
There is a compression if the value of b is greater than 1.
To find the value of coordinates after horizontal dilation, divide the original coordinates of the graph with the value of b
The horizontal dilation factor is a reciprocal of the b value
Vertical
Represented by a in the formula: a(bx - h)^2 + k
There is a stretch when the value of a is greater than 1
There is a compression if the value of a is between 0 and 1
To find the value of coordinates after vertical dilation, multiply the original coordinates of a graph with the value of a
The vertical dilation factor is the same as the value of a
When translating the graph, always start with dilation or reflection
