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Evaluate the function [tex]g(x) = -2x^2 + 3x - 5[/tex] for the input values [tex]-2[/tex], [tex]0[/tex], and [tex]3[/tex].

1. For [tex]g(-2)[/tex]:
[tex]\[
\begin{array}{l}
g(-2) = -2(-2)^2 + 3(-2) - 5 \\
g(-2) = -2(4) + (-6) - 5 \\
g(-2) = -8 - 6 - 5 \\
g(-2) = \boxed{-19}
\end{array}
\][/tex]

2. For [tex]g(0)[/tex]:
[tex]\[
g(0) = -2(0)^2 + 3(0) - 5 \\
g(0) = 0 + 0 - 5 \\
g(0) = \boxed{-5}
\][/tex]

3. For [tex]g(3)[/tex]:
[tex]\[
g(3) = -2(3)^2 + 3(3) - 5 \\
g(3) = -2(9) + 9 - 5 \\
g(3) = -18 + 9 - 5 \\
g(3) = \boxed{-14}
\][/tex]

Sagot :

GinnyAnswer
Let's evaluate the function [tex]\( g(x) = -2x^2 + 3x - 5 \)[/tex] for the input values [tex]\(-2\)[/tex], [tex]\(0\)[/tex], and [tex]\(3\)[/tex].

### Step-by-Step Solutions:

#### 1. Evaluating [tex]\( g(-2) \)[/tex]:
[tex]\[ g(-2) = -2(-2)^2 + 3(-2) - 5 \][/tex]
First, calculate [tex]\((-2)^2\)[/tex]:
[tex]\[ (-2)^2 = 4 \][/tex]
Now multiply by [tex]\(-2\)[/tex]:
[tex]\[ -2 \cdot 4 = -8 \][/tex]
Next, calculate [tex]\(3 \cdot (-2)\)[/tex]:
[tex]\[ 3 \cdot (-2) = -6 \][/tex]
Finally, sum all terms:
[tex]\[ g(-2) = -8 - 6 - 5 = -19 \][/tex]

So,
[tex]\[ g(-2) = -19 \][/tex]

#### 2. Evaluating [tex]\( g(0) \)[/tex]:
[tex]\[ g(0) = -2(0)^2 + 3(0) - 5 \][/tex]
First, calculate [tex]\(0^2\)[/tex]:
[tex]\[ 0^2 = 0 \][/tex]
Now multiply by [tex]\(-2\)[/tex]:
[tex]\[ -2 \cdot 0 = 0 \][/tex]
Next, calculate [tex]\(3 \cdot 0\)[/tex]:
[tex]\[ 3 \cdot 0 = 0 \][/tex]
Finally, sum all terms:
[tex]\[ g(0) = 0 + 0 - 5 = -5 \][/tex]

So,
[tex]\[ g(0) = -5 \][/tex]

#### 3. Evaluating [tex]\( g(3) \)[/tex]:
[tex]\[ g(3) = -2(3)^2 + 3(3) - 5 \][/tex]
First, calculate [tex]\(3^2\)[/tex]:
[tex]\[ 3^2 = 9 \][/tex]
Now multiply by [tex]\(-2\)[/tex]:
[tex]\[ -2 \cdot 9 = -18 \][/tex]
Next, calculate [tex]\(3 \cdot 3\)[/tex]:
[tex]\[ 3 \cdot 3 = 9 \][/tex]
Finally, sum all terms:
[tex]\[ g(3) = -18 + 9 - 5 = -14 \][/tex]

So,
[tex]\[ g(3) = -14 \][/tex]

### Final Results:
[tex]\[ \begin{array}{l} g(-2) = -19 \\ g(0) = -5 \\ g(3) = -14 \\ \end{array} \][/tex]
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