The function \( y = -3x^2 \) is shifted 2 units towards the positive x-axis (right) and 3 units towards the positive y-axis (up). Find the resulting function.
Show Hint
- \( y = 3x^2 + 5 \)
- \( y = 3x^2 \)
- \( y = 3(x + 2)^2 + 3 \)
- \( y = 3(x - 2)^2 - 3 \)
- \( y = 3(x - 2)^2 + 3 \)
The Correct Option is
Solution and Explanation
To shift the function \( y = -3x^2 \) 2 units to the right, replace \( x \) with \( x - 2 \): \[ y = -3(x - 2)^2. \]
Step 2: Shift the function vertically.
To shift the function 3 units up, add 3 to the equation: \[ y = -3(x - 2)^2 + 3. \]
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