SOLUTION: The graph of y = √ 2x is translated by the vector (-5,3).Find the equation of the resulting graph.

Algebra ->  Graphs -> SOLUTION: The graph of y = √ 2x is translated by the vector (-5,3).Find the equation of the resulting graph.      Log On


   

Question 1200542: The graph of y = √ 2x is translated by the vector (-5,3).Find the equation of the resulting
graph.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: y+=+sqrt%282x%2B10%29%2B3

Work Shown:
y+=+sqrt%282x%29

y+=+sqrt%282%28x%2B5%29%29

y+=+sqrt%282%28x%2B5%29%29%2B3

y+=+sqrt%282x%2B10%29%2B3

Explanation:
The translation vector is (-5,3).
It means "shift 5 units left and 3 units up"
In the 2nd step shown above, we replace x with (x+5) to shift 5 units to the left.
In the 3rd step, the +3 at the end shifts the entire curve up 3 units.

Graph

y+=+sqrt%282x%29 in red
y+=+sqrt%282%28x%2B5%29%29 in green (shift 5 units left)
y+=+sqrt%282%28x%2B5%29%29%2B3 in blue (shifted 3 units up)

Desmos and GeoGebra are two graphing options I recommend.