Question

What is the domain and range of the parabola with the equation y = 0.5(x² – 12x – 6)?

a) D: (–[infinity], –21]; R: (–[infinity], [infinity])
b) D: [–21, [infinity]); R: (–[infinity], [infinity])
c) D: (–[infinity], [infinity]); R: [–21, [infinity])
d) D: (–[infinity], [infinity]); R: (–[infinity], –21]

Answer 1

The domain of the parabola is (-∞, ∞) and the range is (-∞, -66].

Step-by-step explanation:

The given equation represents a parabola. To find the domain and range, we consider the values that x can take and the corresponding values of y. The domain of the parabola is the set of all possible x-values, while the range is the set of all possible y-values.

For this parabola equation, y = 0.5(x² – 12x – 6), there are no restrictions on the values that x can take. Therefore, the domain is (-∞, ∞). The range, on the other hand, can be found by considering the vertex of the parabola. The vertex is found using the formula x = -b/2a and then plugging that value into the equation to find the corresponding y-value. In this case, the vertex occurs at x = 12/2(0.5) = 12.

Plugging x = 12 into the equation, we get y = 0.5(12² – 12(12) – 6) = -66. Therefore, the range is (-∞, -66].