Final answer:
To write the equation of a quadratic that has been reflected across the x-axis, vertically stretched by a factor of 3, and shifted 4 units down, start with the general form of a quadratic equation and make the necessary adjustments.
Step-by-step explanation:
To write the equation of a quadratic that has been reflected across the x-axis, vertically stretched by a factor of 3, and shifted 4 units down, you can start with the general form of a quadratic equation: y = ax^2 + bx + c. Since the equation has been reflected across the x-axis, the value of 'a' will be negative. The equation can be written as y = -3ax^2 + bx + c - 4.
For example, if we want to reflect the quadratic equation y = x^2 across the x-axis, vertically stretch it by a factor of 3, and shift it 4 units down, the equation becomes y = -3x^2 - 4.