Question

Identify the maximum or minimum value and the domain and range of the graph of the function y = 2(x + 2)^2 - 3

A. minimum value: 3
domain: all real numbers 3
range: all real numbers


B. maximum value: -3
domain: all real numbers ≤ 3
range: all real numbers



C. minimum value: -3
domain: all real numbers
range: all real numbers ≥ -3


D. maximum value: 3
domain: all real numbers
range: all real numbers ≤ 3

Answer 1

A. minimum value: 3

domain: all real numbers 3

range: all real numbers

Explanation:

I just took the quick check

Answer 2

y = 2(x + 2)^2 - 3 has the form y = a(x-h)^2 + k.

Here, a=2, h=-2 and k=-3.

This is a quadratic function. Its graph is a vertical one which opens up (we know that because a = 2 is positive). Its vertex is (-2, -3). Because the graph opens up, (-2, -3) represents the minimum of this function.

The domain of any and all polynomial(s) includes "all real numbers."
The range is the set of possible outputs (y-values) and is (-3, infinity).