Final answer:
The graph of y = x^2 is transformed into y = -x^2 - 3 by reflecting it over the x-axis and translating it down by 3 units.
Step-by-step explanation:
The student is asking about the transformation of the function y = x^2 into the function y = -x^2 - 3. This involves a reflection and a translation of the original graph. To start with, the negative sign in front of the x^2 term indicates that the graph is reflected vertically over the x-axis. This changes the direction of the parabola from opening upwards to opening downwards.
After reflecting the graph of y = x^2, the subtraction of 3 from the equation indicates that the graph is translated vertically downwards by 3 units. This means that every point on the graph y = x^2 is moved 3 units down to get the graph of y = -x^2 - 3.
In summary, the graph of y = x^2 is transformed into the graph of y = -x^2 - 3 by first reflecting it vertically across the x-axis, which results in an upside-down parabola, and then translating it downwards by 3 units along the y-axis.