Given that \( g(x)=3 x^{2}-4 x+10 \), find each of the following. a) \( g(0) \) b) \( g(-2) \) c) \( g(3) \) d) \( g(-x) \) e) \( g(1-t) \)

Let's calculate the values step by step: a) To find \( g(0) \): \[ g(0) = 3(0)^2 - 4(0) + 10 = 0 - 0 + 10 = 10 \] b) To find \( g(-2) \): \[ g(-2) = 3(-2)^2 - 4(-2) + 10 = 3(4) + 8 + 10 = 12 + 8 + 10 = 30 \] c) To find \( g(3) \): \[ g(3) = 3(3)^2 - 4(3) + 10 = 3(9) - 12 + 10 = 27 - 12 + 10 = 25 \] d) To find \( g(-x) \): \[ g(-x) = 3(-x)^2 - 4(-x) + 10 = 3(x^2) + 4x + 10 = 3x^2 + 4x + 10 \] e) To find \( g(1-t) \): \[ g(1-t) = 3(1-t)^2 - 4(1-t) + 10 \] Calculating \( (1-t)^2 \) first: \[ (1-t)^2 = 1 - 2t + t^2 \] Now plug it back: \[ g(1-t) = 3(1 - 2t + t^2) - 4(1 - t) + 10 \] Expanding this: \[ = 3 - 6t + 3t^2 - 4 + 4t + 10 \] Combining the like terms: \[ = 3t^2 - 2t + 9 \] So, to summarize, the answers are: a) \( g(0) = 10 \) b) \( g(-2) = 30 \) c) \( g(3) = 25 \) d) \( g(-x) = 3x^2 + 4x + 10 \) e) \( g(1-t) = 3t^2 - 2t + 9 \)