i-03 transformations warm-up · 11. translated 3 units left and 4 units down 12. translated 7 units...
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Name _________________________________________ Date ________________ Hour _____________
I-03 Transformations
Warm-Up: Graph each equation using a table of values. Identify the axis of symmetry, vertex, domain
and range.
1. 𝑦 = −(𝑥 + 2)2 + 7
Axis of symmetry: _________
Vertex: _________
Domain: _____________
Range: _____________
2. 𝑦 = 3(𝑥 − 1)2
Axis of symmetry: _________
Vertex: _________
Domain: _____________
Range: _____________
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Transformations from the Parent Function
• The most simplistic quadratic equation is _________________
• This is known as the ______________________________________
• A transformation is a _______________ to the _____________ or ______________ of a figure
Examples: Graph each function describe how it compares to the parent function shown on the
graph.
Parent Function: 𝑦 = 𝑥2
Vertex:
3. 𝑦 = (𝑥 + 2)2
Vertex:
Transformations:
4. 𝑦 = 𝑥2 + 5
Vertex:
Transformations:
5. 𝑦 = (𝑥 + 1)2 − 6
Vertex:
Transformations:
6. 𝑦 = −(𝑥 − 4)2 + 1
Vertex:
Transformations:
7. 𝑦 = 3𝑥2 − 7
Vertex:
Transformations:
8. 𝑦 = −1
2(𝑥 − 3)2 − 2
Vertex:
Transformations:
Putting It Together
Given a quadratic equation in vertex form, 𝑓(𝑥) = 𝑎(𝑥 − ℎ)2 + 𝑘
• ℎ is the __________________________ shift; + shifts ____________, − shifts ____________
• 𝑘 is the __________________________ shift; + shifts ____________, − shifts ____________
• If 𝑎 is negative, the graph is _____________________ across the ______________
• |𝑎| > 1 represents a vertical ___________________
• 0 < |𝑎| < 1 represents a vertical ___________________
Writing Equations: Transformations from the parent functions 𝑦 = 𝑥2 are described below. Write an
equation to represent the function.
9. translated 2 units right
10. translated 5 units up
11. translated 3 units left and 4 units down 12. translated 7 units right and 4 units up
13. reflected over the x-axis, then translated 3
units down
14. reflected over the x-axis, then translated 5
units right and 2 units down
15. vertically compressed by a factor of 1
3, then
translated 8 units up
16. vertically stretched by a factor of 2,
reflected over the x-axis, then translated 4 units
left