Chapter 1 Section 4
Geometric Transformations
Shift Formulas:
Vertical ® y = f(x) + c moves up c units
y = f(x) - c moves down c units
Horizontal ® y = f(x-c) moves right c units
y = f(x+c) moves left c units
Stretch
or Shrink Formulas
Vertical ®
y = c f(x) c>1 stretches vertically by c units
y = c f(x) 0<c<1 shrinks vertically by c units
Horizontal ®
y = f(cx) c>1 shrinks horizontally by 1/c units
y = f(cx) 0<c<1 stretches horizontally by 1/c units
Reflection Formulas:
y = f(x) then y = f(-x) reflects across y-axis
y = f(x) then y = -f(x) reflects across x-axis
The Parabola
y = ax2+ bx + c
|
Vertex is |
(- |
b |
c- |
b2 | ) |
| 2a , | 4a |
Ex: y = 3x2 + 12x - 6
|
Vertex is |
(- |
12 |
-6- |
122 | ) |
| 2(3), | 4(3) |
Vertex is (-2,-18)
y = (x-h)2 + k
vertex is (h,k)
(Same example using completing the
square)
Ex: y = 3x2 + 12x - 6
3(x2 + 4x +4-4) - 6
3(x +4x + 4) - 12 - 6
3(x +2) - 18
Vertex is (-2,-18)
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