To shift the graph of the quadratic function y = 3x² one unit to the left and two units upward, we need to modify the equation accordingly. Shifting the graph to the left by 1 unit involves replacing x with (x + 1), and shifting it upward by 2 units involves adding 2 to the entire equation. Therefore, the equation of the shifted quadratic function would be:
y = 3 ( x + 1 )² + 2
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Answers & Comments
1. **Horizontal Shift Left (1 unit):** Replace \(x\) with \((x + 1)\).
2. **Vertical Shift Upward (2 units):** Add 2 to the entire function.
So, the equation of the shifted quadratic function is \(y = 3(x + 1)^2 + 2\).
Verified answer
To shift the graph of the quadratic function y = 3x² one unit to the left and two units upward, we need to modify the equation accordingly. Shifting the graph to the left by 1 unit involves replacing x with (x + 1), and shifting it upward by 2 units involves adding 2 to the entire equation. Therefore, the equation of the shifted quadratic function would be:
y = 3 ( x + 1 )² + 2