Inside versus outside shifts
Adding 2 outside x² moves the graph up two units. Replacing x by moves it left two units; input changes act differently from output changes.
Algebra / English
Transforming Algebraic Functions: Shifting, Stretching, and Reflecting
Professor Dave Explains · YouTube · 7:51
YouTube · Professor Dave ExplainsOriginal video
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Transform function graphs using shifts, stretches and reflections, then combine the changes in a parabola.
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0:00Inside versus outside shifts3:00Stretch and reflect4:30Combine transformationsLearning script
Generated from the video's visuals and explanation; not verbatim speech.
Adding 2 outside x² moves the graph up two units. Replacing x by moves it left two units; input changes act differently from output changes.
Multiplying the function output by 2 doubles vertical distances from the horizontal axis. A negative outside multiplier also reflects the graph across that axis.
The graph of −²+4 comes from x² by shifting right three, stretching vertically by two and reflecting, then shifting up four. Its vertex is (3,4).
Knowledge cards
Stretch and reflect
Multiplying the function output by 2 doubles vertical distances from the horizontal axis. A negative outside multiplier also reflects the graph across that axis.
Combine transformations
The graph of −²+4 comes from x² by shifting right three, stretching vertically by two and reflecting, then shifting up four. Its vertex is (3,4).
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- Functions ExplanationAt 0:00
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Adding 2 outside x² moves the graph up two units. Replacing x by moves it left two units; input changes act differently from output changes. Multiplying the function output by 2 doubles vertical distances from the horizontal axis. A negative outside multiplier also reflects the graph across that axis. The graph of −²+4 comes from x² by shifting right three, stretching vertically by two and reflecting, then shifting up four. Its vertex is (3,4).
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