The graph of y = x^2 is shifted 4 units to the right. This graph is then vertically stretched by a factor of 5 and reflected across the x-axis. Finally, the graph is shifted 8 units upward.
Give the equation of the function whose graph is described.
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y = x2
To shift 4 units to the right, replace x with (x-4). (To shift left, replace x with (x+4))
y = (x-4)2
To stretch vertically by a factor of 5, multiply (x-4) by 5
y = 5(x-4)2
To reflect across the x-axis, change the sign of 5
y = -5(x-4)2
To shift up by 8, simply add 8 to the expression:
y = -5(x-4)2 + 8
Finally, multiply out the term -5(x-4)2 and simplify to get the answer.