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The function y=3x2 is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up). Find the resulting function.
A. y=3x2+5
B. y=3x2
C. y=3(x+2)2+3
D. y=3(x-2)2-3
E. y=3(x-2)2+3
- a)A
- b)B
- c)C
- d)D
- e)E
Correct answer is option 'E'. Can you explain this answer?
Verified Answer
The function y=3x2is shifted 2 units towards the positive x-axis (righ...
The upward shift is simply addressed by adding three in the given function, and the horizontal shift is addressed by changing the value of x in the given function. If the shift is a units towards right, then we replace x with x-a. If the shift is towards left then we replace x with x+a.
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Most Upvoted Answer
The function y=3x2is shifted 2 units towards the positive x-axis (righ...
Given information:
- The original function is y=3x^2
- The function is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up)
To find the resulting function, we need to apply the following transformations to the original function:
- Horizontal shift: x → x-2 (2 units towards the positive x-axis)
- Vertical shift: y → y+3 (3 units towards the positive y-axis)
Solution:
We can apply these transformations directly to the function y=3x^2 as follows:
y = 3(x-2)^2 + 3
This is because the vertex form of a quadratic function is y=a(x-h)^2+k, where (h,k) is the vertex of the parabola, and a determines the direction and magnitude of the opening of the parabola.
In this case, the vertex of the original function y=3x^2 is (0,0), and a=3, which means the parabola opens upwards. After the transformations, the vertex of the resulting function y=3(x-2)^2+3 is (2,3), which means the parabola is shifted 2 units towards the positive x-axis and 3 units towards the positive y-axis, and still opens upwards with the same magnitude.
Therefore, the resulting function is y=3(x-2)^2+3, which is option E.
- The original function is y=3x^2
- The function is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up)
To find the resulting function, we need to apply the following transformations to the original function:
- Horizontal shift: x → x-2 (2 units towards the positive x-axis)
- Vertical shift: y → y+3 (3 units towards the positive y-axis)
Solution:
We can apply these transformations directly to the function y=3x^2 as follows:
y = 3(x-2)^2 + 3
This is because the vertex form of a quadratic function is y=a(x-h)^2+k, where (h,k) is the vertex of the parabola, and a determines the direction and magnitude of the opening of the parabola.
In this case, the vertex of the original function y=3x^2 is (0,0), and a=3, which means the parabola opens upwards. After the transformations, the vertex of the resulting function y=3(x-2)^2+3 is (2,3), which means the parabola is shifted 2 units towards the positive x-axis and 3 units towards the positive y-axis, and still opens upwards with the same magnitude.
Therefore, the resulting function is y=3(x-2)^2+3, which is option E.
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The function y=3x2is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up). Find the resulting function.A. y=3x2+5B. y=3x2C. y=3(x+2)2+3D. y=3(x-2)2-3E. y=3(x-2)2+3a)Ab)Bc)Cd)De)ECorrect answer is option 'E'. Can you explain this answer?
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