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.