Final answer:
The parametric equations that represent y = -|x| are option (B) (x, -|x|) and option (D) (-x, -x²).
Step-by-step explanation:
The parametric equations that represent y = -|x| are option (B) (x, -|x|) and option (D) (-x, -x²).
To understand this, we first need to understand the absolute value function. The absolute value function, denoted as |x|, returns the distance of a number from zero. When we have a negative value for x, the absolute value will make it positive. So, for each value of x, we need to consider the sign of x and then negate it to get -|x|.
We can achieve this using either option (B) or option (D). In both cases, the x-coordinate remains the same, but for option (B), the y-coordinate is the negation of the absolute value of x, while for option (D), the y-coordinate is the negation of the square of x. Both options represent the graph of y = -|x|.