1. ## Finding parabolic equation

Given the parabola f(x)=ax^2 we are moving it one unit on the x-axis, and two units on the y-axis. What would be the equation of the new parabola ?
I got a hunch it would be f(x)=a(x-1)^2 + 2 but I would be grateful if someone could explain the solution and the way I approach such questions.

2. Originally Posted by leonig01
Given the parabola f(x)=ax^2 we are moving it one unit on the x-axis, and two units on the y-axis. What would be the equation of the new parabola ?
I got a hunch it would be f(x)=a(x-1)^2 + 2 but I would be grateful if someone could explain the solution and the way I approach such questions.
Correct.

3. Originally Posted by leonig01
Given the parabola f(x)=ax^2 we are moving it one unit on the x-axis, and two units on the y-axis. What would be the equation of the new parabola ?
I got a hunch it would be f(x)=a(x-1)^2 + 2 but I would be grateful if someone could explain the solution and the way I approach such questions.
You have got the right answer there, and for parabola graphs you follow the same methods as you would for normal:

$\displaystyle y=f(x-a)$ is a shift of plus a along the x-axis, as seen in the $\displaystyle a(x-1)^2$ part of the equation.

$\displaystyle y=f(x)+a$ is a shift of plus a along the y-axis, as seen in the $\displaystyle + 2$ part of the equation.

The way you approached the question was fine, it is simply a question of remembering the rules

Hope this helps explain it a bit

Craig