Advanced MathVery hardTranslating a parabola then evaluating
Advanced Math practice question
The graph of y = x² is shifted 3 units to the right and 2 units down. The new graph passes through the point (5, a). What is the value of a?
Answer: 2
The new equation is y = (x − 3)² − 2. At x = 5: (2)² − 2 = 2.
Common wrong answers
- If you answered 6
- A right shift subtracts inside the square: (5 − 3)², not (5 + 3)² scaled.
- If you answered 27
- Shifting right means (x − 3)², so x = 5 gives 4 − 2 = 2, not (5 + 3)² type values.
- If you answered -2
- −2 is the vertical shift; evaluate the whole rule at x = 5.
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