Question

What are the vortex, the axis of symmetry, the minimum or the maximum, the domain, and the range of y=−5⋅(x+2)^2 −8?

a) Vortex: (-2, -8); Axis of Symmetry: x = -2; Minimum: -8; Domain: All Real Numbers; Range: (−8,[infinity])
b) Vortex: (-2, -8); Axis of Symmetry: x = -2; Maximum: -8; Domain: All Real Numbers; Range: (−[infinity],−8)
c) Vortex: (-2, -8); Axis of Symmetry: x = -2; Minimum: -8; Domain: (−2,[infinity]); Range: (−8,[infinity])
d) Vortex: (-2, -8); Axis of Symmetry: x = -2; Maximum: -8; Domain: (−2,[infinity]); Range: (−[infinity],−8)

Answer 1

The vortex, axis of symmetry, minimum value, domain, and range of the function y = -5(x+2)^2 -8 are (-2, -8), x = -2, -8, All Real Numbers, and (-8, [infinity]) respectively.

Step-by-step explanation:

The vortex of the equation y = -5(x+2)^2 -8 is the point (-2, -8). The axis of symmetry is the vertical line x = -2. The equation represents a quadratic function with a vertex at the vortex point, so it opens downwards and has a minimum value. In this case, the minimum value is -8. The domain of the function is all real numbers, and the range is (-8, [infinity]).