Help me please.

Which of the following accurately depicts the transformation of y=x^2 to the function shown below?

y=5(x-2)^2+1

A. Shift 5 units right, stretch vertically by a factor of 2, then shift up 1 unit.

B. Shift up 1 unit, stretch horizontally by a factor of 5, then shift left 2 units.

C. Shift right 2 units, shrink vertically to 1/5 of the original height, then shift up 1 unit.

D. Shift right 2 units, stretch vertically by a factor of 5, then shift up 1 unit.

x^2

(x-2)^2 shift right 2
5(x-2)^2 stretch vertically by 5
5(x-2)^2+1 shift up 1

That should help decide.

Thanks.

A. Shift 5 units right, stretch vertically by a factor of 2, then shift up 1 unit. Because if you look at it from the perspective of the graph, it's like the original function went on a wild adventure. First, it decided to take a little jog to the right, 5 units to be precise. Then, feeling a bit adventurous, it decided to stretch vertically by a factor of 2, making it twice as tall as before. And just when you thought the fun was over, it had one more trick up its sleeve - it shifted up the vertical axis by 1 unit. That's quite the transformation for a little quadratic function, don't you think?

The correct answer is:

A. Shift 5 units right, stretch vertically by a factor of 2, then shift up 1 unit.

Explanation:

To transform the function y=x^2 to y=5(x-2)^2+1, we can break down the steps as follows:

1. Shift 5 units right: This means the graph is shifted horizontally to the right by 5 units, and the x-values are increased by 5.

2. Stretch vertically by a factor of 2: The coefficient 5 stretches the graph vertically by a factor of 5, making it taller. The original function y=x^2 would become y=5x^2.

3. Shift up 1 unit: The constant term 1 shifts the graph vertically upwards by 1 unit.

Therefore, the transformation is a shift of 5 units right, followed by a vertical stretch by a factor of 2, and finally a shift up by 1 unit. Hence, the correct answer is A.

To determine the correct transformation, let's break down the given function, y = 5(x - 2)^2 + 1, and compare it to the original function, y = x^2.

The transformations in the order they occur are:
1. Shift right 2 units
2. Vertical stretch by a factor of 5
3. Shift up 1 unit

Now, let's compare this with the answer choices:
A. Shift 5 units right, stretch vertically by a factor of 2, then shift up 1 unit.
B. Shift up 1 unit, stretch horizontally by a factor of 5, then shift left 2 units.
C. Shift right 2 units, shrink vertically to 1/5 of the original height, then shift up 1 unit.
D. Shift right 2 units, stretch vertically by a factor of 5, then shift up 1 unit.

By comparing the transformations, we can see that the correct answer is option D. It accurately depicts the transformation of y = x^2 to the function y = 5(x - 2)^2 + 1.