Question

If I wanted to change the y-intercept of a quadratic from (0,2) to (0,5), which transformation explains what happened to the graph?

Answer 1

Many transformations will affect the y-intercept of a quadratic.  However, the most obvious one is translation, which moves the whole quadratic up (or down if k<0) by an amount k.
The transformation is 
T(0,k)f(x) -> f(x)+k

For example, the quadratic f(x)=x^2+2x+2 (y-intercept = 2) will be transformed to f(x)->f(x)+(5-2)=f(x)+3=x^2+2x+5.