If the parent function f(x) = x2 is vertically stretched by a factor of 2, translated 14 units to the right, then
translated 6 units up, write the resulting function g(x) in vertex form.
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Please present "square of x" as x^2 or as\[x^2,\] Not as x2. Thanks.
The standard, vertex equation of a parabola is \[y-k=a(x-h)^2.\]
If the vertex is initially at the origin (0,0), then h=0 and k=0, so that the initial equation of the parabola is y=ax^2.
You are told that the graph of y our parabola is stretched vertically by a factor of 2. How will that affect y=ax^2?
You are told that the graph is translated (moved) 14 units to the right and 6 units up. How will that affect y=ax^2? Hint: start using the equation \[y-k=a(x-h)^2.\] now.