if g (x) = 2x² - 6x + 1, then find the following...

a. g (0)
b. g (b)
c. g (3)

Given the function \( g(x) = 2x^2 - 6x + 1 \), we will find the following values:

### a. \( g(0) \)

Substitute \( x = 0 \) into the function:
\[ g(0) = 2(0)^2 - 6(0) + 1 \]
\[ g(0) = 0 - 0 + 1 \]
\[ g(0) = 1 \]

### b. \( g(b) \)

Substitute \( x = b \) into the function:
\[ g(b) = 2(b)^2 - 6(b) + 1 \]
\[ g(b) = 2b^2 - 6b + 1 \]

### c. \( g(3) \)

Substitute \( x = 3 \) into the function:
\[ g(3) = 2(3)^2 - 6(3) + 1 \]
\[ g(3) = 2(9) - 18 + 1 \]
\[ g(3) = 18 - 18 + 1 \]
\[ g(3) = 1 \]

Thus, the values are:
- \( g(0) = 1 \)
- \( g(b) = 2b^2 - 6b + 1 \)
- \( g(3) = 1 \)

Would you like more details or have any questions about these calculations?

Here are some related questions you might find interesting:

1. What is the vertex form of the function \( g(x) \)?
2. How would you find the roots of \( g(x) \)?
3. What is the axis of symmetry for the function \( g(x) \)?
4. What are the coordinates of the vertex of \( g(x) \)?
5. How would you graph \( g(x) \)?
6. What is the value of \( g(x) \) when \( x = -1 \)?
7. How does the function \( g(x) \) change if the constant term is altered?
8. What is the derivative of \( g(x) \) with respect to \( x \)?

**Tip:** When evaluating a function for a specific value, always substitute the given value directly into the function and simplify step by step.

Learn how to evaluate the quadratic function g(x) = 2x^2 - 6x + 1 for specific values of x. This problem demonstrates the application of the quadratic function formula and its evaluation steps. Suitable for students in Grades 9-12.

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