What is the range of y = 3(x+4)^2 - 2

Question

A. all real numbers

B. y ≥ -2

C. y ≤ -2

D. y ≥ 2 

Answer 1

The function y = 3(x + 4)^2 - 2.

The above function represents vertex form of parabola : y = a (x - h )^2 + k .

 a  = 3 , h  = - 4 and k  = - 2.

a  is positive number the parabola opens up ward, and has minimum value.

When the parabola opens upward, it has a minimum point which is the vertex of parabola (-  4, - 2)

We know that domain of the function is all possible x  values and range is all posible y  values.

Parabola domain x  =  all real numbers.

In the minimum point y  = - 2, the graph of parabola cannot be lower than - 2.

Thus the range of function y  ≥ - 2.

Domain of function is all real numbers.

Range of the function is  {y |y  ≥ - 2}.

Option B is the correct choise.