SOLUTION: Find g(x), where g(x) is the translation 3 units left of f(x)=x2. Write your answer in the form a(x - h)2+k, where a, h, and k are integers.

Algebra ->  Rational-functions -> SOLUTION: Find g(x), where g(x) is the translation 3 units left of f(x)=x2. Write your answer in the form a(x - h)2+k, where a, h, and k are integers.       Log On


   

Question 1204394: Find g(x), where g(x) is the translation 3 units left of f(x)=x2.
Write your answer in the form a(x - h)2+k, where a, h, and k are integers.

Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: g(x) = (x+3)^2

Explanation:
Imagine that the parabola is stuck in place. What's allowed to move is only the xy axis. If we moved the xy axis 3 units to the right, then it gives the illusion the parabola moves 3 units to the left.

To move the xy axis 3 units to the right, we replace each old input x with the new input x+3.
This will mean x^2 updates to (x+3)^2 as the answer.

A point like the vertex (0,0) on f(x) moves 3 units to the left to arrive at (-3,0) on g(x).

Graph
graph%28400%2C400%2C-6%2C4%2C-5%2C5%2C-1000%2Cx%5E2%2C%28x%2B3%29%5E2%29
f(x) = x^2 in green
g(x) = (x+3)^2 in blue

GeoGebra and Desmos are two graphing tools I recommend.