Question

evaluate the function $g(x) = -2x^2 + 3x - 5$ for the input values $-2$, $0$, and $3$.
$g(-2) = -2(-2)^2 + 3(-2) - 5$
$g(-2) = -2(4) - 6 - 5$
$g(-2) = \square$
$g(0) = \square$
$g(3) = \square$

Explanation:

Step1: Calculate $g(-2)$

Substitute $x=-2$ into $g(x)$:
$$g(-2) = -2(-2)^2 + 3(-2) - 5 = -2(4) -6 -5$$
$$g(-2) = -8 -6 -5$$

Step2: Simplify $g(-2)$

$$g(-2) = -19$$

Step3: Calculate $g(0)$

Substitute $x=0$ into $g(x)$:
$$g(0) = -2(0)^2 + 3(0) - 5 = 0 + 0 -5$$

Step4: Simplify $g(0)$

$$g(0) = -5$$

Step5: Calculate $g(3)$

Substitute $x=3$ into $g(x)$:
$$g(3) = -2(3)^2 + 3(3) - 5 = -2(9) +9 -5$$
$$g(3) = -18 +9 -5$$

Step6: Simplify $g(3)$

$$g(3) = -14$$

Answer:

$g(-2) = -19$
$g(0) = -5$
$g(3) = -14$