Answer:
The resulting equation is [tex]g(x) = 7\cdot (x+5)^{2}-2[/tex].
Step-by-step explanation:
[tex]g(x)[/tex] is obtained by making three operation on parent function [tex]f(x)[/tex], whose procedured is presented below:
Streching
[tex]f'(x) = k\cdot f(x)[/tex], where [tex]k > 0[/tex]
Horizontal shift
[tex]f''(x) = f'(x+r)[/tex], where [tex]r > 0[/tex] when [tex]f'[/tex] is translated leftwards (+x direction), otherwise it is translated rightwards (-x direction).
Vertical shift
[tex]g(x) = f''(x)+c[/tex], where [tex]c > 0[/tex] when [tex]f''[/tex] is translated upwards (+y direction), otherwise it is translated downwards. (-y direction)
If [tex]f(x) = x^{2}[/tex], then [tex]g(x)[/tex] is:
Stretching
[tex]f'(x) = 7\cdot x^{2}[/tex]
Horizontal shift
[tex]f''(x) = 7\cdot (x+5)^{2}[/tex]
Vertical shift
[tex]g(x) = 7\cdot (x+5)^{2}-2[/tex]
The resulting equation is [tex]g(x) = 7\cdot (x+5)^{2}-2[/tex].
