Using the parent function y=x2
Shift 4 units up
Shift 4 units down
Shift 4 units to the right
Shift 4 units to the left
Answer choices: y= (x+4)^2, y=x^2=4, y=x^2+4, y=(x-4)^2
To shift the parent function y = x^2 four units up, we can add 4 to the function. So the answer is y = x^2 + 4.
To shift the parent function y = x^2 four units down, we can subtract 4 from the function. So the answer is y = x^2 - 4.
To shift the parent function y = x^2 four units to the right, we can replace x with (x - 4) in the function. So the answer is y = (x - 4)^2.
To shift the parent function y = x^2 four units to the left, we can replace x with (x + 4) in the function. So the answer is y = (x + 4)^2.
To shift the parent function y=x^2, we can use the following transformations:
1. Shift 4 units up: To shift the function 4 units up, we add 4 to the y-values of the parent function. The equation for this transformation is y=x^2+4.
2. Shift 4 units down: To shift the function 4 units down, we subtract 4 from the y-values of the parent function. The equation for this transformation is y=x^2-4.
3. Shift 4 units to the right: To shift the function 4 units to the right, we subtract 4 from the x-values of the parent function. The equation for this transformation is y=(x-4)^2.
4. Shift 4 units to the left: To shift the function 4 units to the left, we add 4 to the x-values of the parent function. The equation for this transformation is y=(x+4)^2.
Therefore, the correct answer choices are:
- Shift 4 units up: y=x^2+4
- Shift 4 units down: y=x^2-4
- Shift 4 units to the right: y=(x-4)^2
- Shift 4 units to the left: y=(x+4)^2
To shift a function up, down, right, or left, you need to modify the equation of the parent function accordingly. Let's start with the parent function y = x^2 and see how each shift affects it.
1. Shift 4 units up:
To shift the function 4 units up, you need to add 4 to the equation. So the answer choice would be y = x^2 + 4.
2. Shift 4 units down:
To shift the function 4 units down, you need to subtract 4 from the equation. So the correct answer choice would be y = x^2 - 4.
3. Shift 4 units to the right:
To shift the function 4 units to the right, you need to replace x with (x - 4) in the equation. So the correct answer choice would be y = (x - 4)^2.
4. Shift 4 units to the left:
To shift the function 4 units to the left, you need to replace x with (x + 4) in the equation. So the correct answer choice would be y = (x + 4)^2.
In summary:
- Shifting the function up by 4 units gives y = x^2 + 4.
- Shifting the function down by 4 units gives y = x^2 - 4.
- Shifting the function to the right by 4 units gives y = (x - 4)^2.
- Shifting the function to the left by 4 units gives y = (x + 4)^2.