Transforming Quadratics
N 6-6
1. Graph y = x2 and y = -x2 using a graphing calculator.
What did the “-“ do to the graph?
_________________________
2. Graph y = x2, y = 2x2, and y = 1 x2 using a graphing calculator.
2
What did the “2” do to the graph?
__________________________
What did the “ 1 ” do to the graph?
2
__________________________
3. Graph y = x2, y = x2 + 4, and y = x2 – 5 using a graphing calculator.
What did the “+ 4” do to the graph?
___________________________
What did the “– 5” do to the graph?
___________________________
N 6-6
4. Graph y = x2, y = (x + 3)2, and y = (x – 4)2 using a graphing
calculator.
What did the “+ 3” do to the graph?
___________________________
What did the “– 4” do to the graph?
___________________________
The equation for a quadratic in Transformation (translation) form is
y = a(x – h)2 + k
…a.k.a. “Vertex” Form…
k is the vertical shift (+ k shifts up, - k shifts down)
h is the horizontal shift ((x - h) shifts right,(x + h) shifts left)… think “opposite”
a is the stretch or shrink factor (a > 1 is a stretch, 0 < a < 1 is a shrink)
-a is a reflection across the x axis
Describe the following transformations on the function y = x2.
5. y = -(x + 2) 2 – 1
6. y = 1 (x – 1) 2
2
7. y = 2x2 + 1
8. y = -3(x – 4) 2 + 2
N 6-6
Write the equation for the quadratic “parent” function with the
following transformations.
9. shift left 4 units and up 1 unit
10. stretch by a factor of 5, shift right 6 units and up 2 units
11. reflect across the x-axis, shift down 5 units
12. shrink by a factor of
1
, reflect across the x-axis, shift right 7 units and
3
down 3 units
Transformations for given Functions…
13. If you wanted to shift y = (x + 2) 2 – 1 up 4 units and left 2 units, what
would be the new equation?
14. If you wanted to shift y = x2 + 3 right 4 units and up 2 units, what would
be the new equation?