Which transformations have been applied to the graph of f(x) = x2 to produce the graph of g(x) = –5x2 + 100x – 450? Select three options.The graph of f(x) = x2 is shifted down 50 units.The graph of f(x) = x2 is shifted up 50 units.The graph of f(x) = x2 is shifted left 10 units.The graph of f(x) = x2 is shifted right 10 units.The graph of f(x) = x2 is reflected over the x-axis.
Answer
A
The graph of f(x) = x2 is shifted down 50 units.
B
The graph of f(x) = x2 is shifted up 50 units.
C
The graph of f(x) = x2 is shifted left 10 units.
D
The graph of f(x) = x2 is shifted right 10 units.
E
The graph of f(x) = x2 is reflected over the x-axis.
Explanation
Complete the square: g(x) = −5x² + 100x − 450 = −5(x − 10)² + 50. The (x − 10) shifts the graph right 10 units, and the +50 shifts it up 50 units. The negative coefficient reflects it over the x-axis; the factor 5 also makes a vertical stretch, which is not one of the listed choices.
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