Question

13.) $g(5) = -5^2 + 3(5) + 2$ $g(5) = $ $g(-3) = -(-3)^2 + 3(-3) + 2$ $g(-3) = $ $g(0) = -0^2 + 3(0) + 2$ $g(0) = $

Explanation:

Step1: Calculate \( G(5) \)

First, handle the exponent: \( -5^2 = -25 \) (note that the exponent applies only to 5, not -5 here), then calculate \( 3(5)=15 \). Now substitute into the formula: \( G(5)= -25 + 15 + 2 \). Then add and subtract: \( -25 + 15 = -10 \), and \( -10 + 2 = -8 \).

Step2: Calculate \( G(-3) \)

First, handle the exponent: \( (-3)^2 = 9 \), so \( -(-3)^2 = -9 \). Then calculate \( 3(-3)= -9 \). Substitute into the formula: \( G(-3)= -9 + (-9) + 2 \). Combine like terms: \( -9 - 9 = -18 \), and \( -18 + 2 = -16 \).

Step3: Calculate \( G(0) \)

Handle the exponent: \( 0^2 = 0 \), so \( -0^2 = 0 \). Then \( 3(0)=0 \). Substitute into the formula: \( G(0)= 0 + 0 + 2 = 2 \).

Answer:

\( G(5) = -8 \), \( G(-3) = -16 \), \( G(0) = 2 \)