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The problem involves a function \( g(x) = 3x^2 - 3x = 20 \), and the goal is to solve for the function values at specific points.

Let me zoom in on the image and interpret the text and choices so I can assist you more effectively.

### Given that \( g(x) = 3x^2 - 3x = 20 \), you need to find:
- a) \( g(1) \)
- b) \( g(-2) \)
- c) \( g(0) \)
- d) \( g(-1) \)
- e) \( g(x-1) \)

I'll solve each one step by step.

### a) \( g(1) \)
Substitute \( x = 1 \) into the function \( g(x) = 3x^2 - 3x \):
\[
g(1) = 3(1)^2 - 3(1) = 3 - 3 = 0
\]
Answer: \( g(1) = 0 \).

### b) \( g(-2) \)
Substitute \( x = -2 \):
\[
g(-2) = 3(-2)^2 - 3(-2) = 3(4) + 6 = 12 + 6 = 18
\]
Answer: \( g(-2) = 18 \).

### c) \( g(0) \)
Substitute \( x = 0 \):
\[
g(0) = 3(0)^2 - 3(0) = 0
\]
Answer: \( g(0) = 0 \).

### d) \( g(-1) \)
Substitute \( x = -1 \):
\[
g(-1) = 3(-1)^2 - 3(-1) = 3(1) + 3 = 3 + 3 = 6
\]
Answer: \( g(-1) = 6 \).

### e) \( g(x - 1) \)
Substitute \( x - 1 \) for \( x \) into \( g(x) = 3x^2 - 3x \):
\[
g(x - 1) = 3(x - 1)^2 - 3(x - 1)
\]
First, expand \( (x - 1)^2 \):
\[
(x - 1)^2 = x^2 - 2x + 1
\]
Now substitute back:
\[
g(x - 1) = 3(x^2 - 2x + 1) - 3(x - 1)
\]
Simplify:
\[
g(x - 1) = 3x^2 - 6x + 3 - 3x + 3 = 3x^2 - 9x + 6
\]
Answer: \( g(x - 1) = 3x^2 - 9x + 6 \).

### Summary of answers:
- a) \( g(1) = 0 \)
- b) \( g(-2) = 18 \)
- c) \( g(0) = 0 \)
- d) \( g(-1) = 6 \)
- e) \( g(x - 1) = 3x^2 - 9x + 6 \)

Would you like any further details or explanations?

#### Relative Questions:
1. How do you determine the value of a quadratic function at a given point?
2. What is the significance of expanding \( (x - 1)^2 \) in part (e)?
3. Can you solve a quadratic equation set to zero to find its roots?
4. What happens if the discriminant of a quadratic function is negative?
5. How can you graph the function \( g(x) = 3x^2 - 3x \) and its transformations?

#### Tip:
When evaluating functions at specific values, substitute the values into the function carefully and simplify step by step.

Given that g(x) = 3x^2 - 3x, find each of the following: a) g(1), b) g(-2), c) g(0), d) g(-1), e) g(x-1).

This page provides a step-by-step solution to evaluating the quadratic function g(x) = 3x^2 - 3x at various points, including g(1), g(-2), g(0), g(-1), and g(x-1). It covers key concepts in algebra, such as quadratic functions, and is suitable for students in Grades 8-10.

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