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.Com
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) (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
f(x) = x^2 in green
g(x) = (x+3)^2 in blue
GeoGebra and Desmos are two graphing tools I recommend.
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