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.

Question

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.

mathmale · Answer

Please present "square of x" as x^2 or as$$x^2,$$    Not as x2.  Thanks.

The standard, vertex equation of a parabola is $$y-k=a(x-h)^2.$$

mathmale · Answer

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.