If you were to vertically stretch the parent function of f(x)=x^2 by a factor of 7, you are basically stretching the the function up or vertically. Because you are stretching the function up, you are changing the y-value of the function which is the variable that shows the vertical axis of a graph, meaning to vertically stretch the function, you must perform 7y or 7(f(x)).
This would mean that your equation must be f(x)=7x^2.