Question

The Graph Of The Function Y = 2x² + X + 1 Is Stretched Vertically About The X-Axis By A Factor Of 2, Stretched Horizontally About The Y-Axis By A Factor Of 5, And Translated 2 Units To The Right And 4 Units Down. Write The Equation Of The Transformed Function.

Answer 1

The transformed function after vertical stretching, horizontal stretching, and translations is given by 4(x - 2)²/25 + 2(x - 2)/5 - 2.

Step-by-step explanation:

When we apply transformations to the function y = 2x² + x + 1, we need to address each transformation step by step. First, we vertically stretch the graph by a factor of 2, which multiplies the entire function by 2 giving us 2(2x² + x + 1) or 4x² + 2x + 2. Next, we horizontally stretch the graph by a factor of 5, which is achieved by dividing the x-values by 5 and replacing x with x/5 in the function, leading to 4(x/5)² + 2(x/5) + 2.

1. Stretched vertically by a factor of 2: Multiply the function by 2, giving y = 4x² + 2x + 2.

2. Stretched horizontally by a factor of 5: Divide x by 5, giving y = 4(x/5)² + 2(x/5) + 2.

3. Translated 2 units to the right and 4 units down: Replace x with (x - 2) and y with (y - 4), giving the transformed function y = 4((x - 2)/5)² + 2((x - 2)/5) + 2 - 4.