Comparing y=(x-h)2 to y=x2
Quadratic Functions Transformations.gsp
1
MPM 2D0
and y = (x ­ h)2 2
Unit 7: Comparing the Graphs of y = x
The graphs will always be compared to the basic function y = x2
For y = (x ­ h)2 If h is positive then.... If h is negative then....
The graph would look like this: The graph would look like this: horizontal
This is called a __________________
_______________________________
translation "right" h units
Equation
y = (x + 14)
y = (x ­ 1)
2
horizontal
This is called a ____________________
_________________________________
translation Left "h" units
h is..... Describe "h" ­14
h is negative Compared to y = x2
2
2
y = (x + 7.5)
For y = (x ­ h)2...
The Maximum or Minimum point occurs at the vertex.
The Vertex is the bottom or top point of the parabola. The point would be (h, 0).
To find the x­intercepts and y­intercepts...
For the x­intercepts, set y = 0. For the y­intercepts, set x = 0 Solve for "x" Solve for "y"
2
Example: y
2
a) Graph y = (x ­ 5) and y = x2 on the same graph. b) Compared to y = x2, the graph
of y = (x ­ 5)2 is horizontally translated ________________
by ______ units.
c) Examine the graph carefully. Complete the following tables for each graph:
For y = x2
For y = (x ­ 5)2
Vertex ( , )
Vertex ( , )
Direction of Opening up or down
Direction of Opening up or down
Vertex
max/min max or min of ___
when x =___
Vertex
max/min x­intercept
x­intercept
y­intercept
y­intercept
Axis of symmetry
x = Axis of symmetry
max or min of ___
when x =___
x = Finding the x and y intercepts for y = (x ­ 5)2
For the x­intercepts, set y = 0 and solve for "x"
For the y­intercepts, set x = 0 and solve for "y"
3
Attachments
Quadratic Functions Transformations.gsp
clipboard.bmp