We are given the function:

$g(x) = 3x^2 - 5x + 10$

Finding Specific Values

1. $g(0)$
   $g(0) = 3(0)^2 - 5(0) + 10 = 10$

2. $g(-2)$
   $g(-2) = 3(-2)^2 - 5(-2) + 10$ $= 3(4) + 10 + 10 = 12 + 10 + 10 = 22$

3. $g(4)$
   $g(4) = 3(4)^2 - 5(4) + 10$ $= 3(16) - 20 + 10 = 48 - 20 + 10 = 38$

Finding Expressions

4. $g(-x)$
   $g(-x) = 3(-x)^2 - 5(-x) + 10$ $= 3x^2 + 5x + 10$

5. $g(1-t)$
   $g(1-t) = 3(1-t)^2 - 5(1-t) + 10$

   Expanding $(1 - t)^2$:
   $(1 - t)^2 = 1 - 2t + t^2$

   Substituting:
   $g(1 - t) = 3(1 - 2t + t^2) - 5(1 - t) + 10$ $= 3 - 6t + 3t^2 - 5 + 5t + 10$ $= 3t^2 - t + 8$

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Would you like a step-by-step breakdown of any part?

Here are five related questions you might find interesting:

1. Find $g(x)$ if $g(x) = 2x^2 - 4x + 7$ and evaluate $g(-3)$.
2. If $g(x) = x^2 - 6x + 9$, simplify $g(a + b)$.
3. Determine whether $g(x) = 3x^2 - 5x + 10$ is an even, odd, or neither function.
4. Find the vertex of the quadratic function $g(x) = 3x^2 - 5x + 10$.
5. Solve for $x$ when $g(x) = 0$ for $g(x) = 3x^2 - 5x + 10$.

Tip:

When evaluating $g(a)$ for any function, always substitute carefully and simplify step by step!