\( \left. \begin{array} { l } { g ( x ) = - 5 x ^ { 2 } - 3 x + 4 } \\ { g ( 2 x ) = \square } \\ { 2 g ( x ) = \square } \\ { g ( x + 2 ) = \square } \\ { g ( x ) + 2 = \square } \\ { g ( x ) + g ( 2 ) = \square } \end{array} \right. \)

We are given the quadratic function   g(x) = –5x² – 3x + 4 and we want to find the following expressions:  1. g(2x)  2. 2g(x)  3. g(x + 2)  4. g(x) + 2  5. g(x) + g(2) Let's compute each one step by step. ────────────────────────────── 1. g(2x) Replace x with 2x in g(x):  g(2x) = –5(2x)² – 3(2x) + 4 First, compute (2x)² = 4x². Then:  g(2x) = –5(4x²) – 6x + 4       = –20x² – 6x + 4 ────────────────────────────── 2. 2g(x) Multiply g(x) by 2:  2g(x) = 2[–5x² – 3x + 4]      = –10x² – 6x + 8 ────────────────────────────── 3. g(x + 2) Replace x with (x + 2) in g(x):  g(x + 2) = –5(x + 2)² – 3(x + 2) + 4 First, expand (x + 2)²:  (x + 2)² = x² + 4x + 4 Now substitute in:  g(x + 2) = –5(x² + 4x + 4) – 3x – 6 + 4        = –5x² – 20x – 20 – 3x – 6 + 4 Combine like terms:  x² term: –5x²  x term: –20x – 3x = –23x  constant term: –20 – 6 + 4 = –22 Thus:  g(x + 2) = –5x² – 23x – 22 ────────────────────────────── 4. g(x) + 2 Simply add 2 to g(x):  g(x) + 2 = (–5x² – 3x + 4) + 2        = –5x² – 3x + 6 ────────────────────────────── 5. g(x) + g(2) First, compute g(2):  g(2) = –5(2)² – 3(2) + 4     = –5(4) – 6 + 4     = –20 – 6 + 4     = –22 Now add g(x) and g(2):  g(x) + g(2) = (–5x² – 3x + 4) + (–22)         = –5x² – 3x – 18 ────────────────────────────── Thus, the answers are:  • g(2x) = –20x² – 6x + 4  • 2g(x) = –10x² – 6x + 8  • g(x + 2) = –5x² – 23x – 22  • g(x) + 2 = –5x² – 3x + 6  • g(x) + g(2) = –5x² – 3x – 18