# Finding parabolic equation

• Jan 5th 2009, 11:01 AM
leonig01
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.
• Jan 5th 2009, 11:02 AM
Mush
Quote:

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.
• Jan 5th 2009, 11:28 AM
craig
Quote:

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
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