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To find the vertex and axis of symmetry for the function \( f(x) = 5 - 6x + 3x^2 \), we can rewrite it in the form \( ax^2 + bx + c \). Here, \( a = 3 \), \( b = -6 \), and \( c = 5 \).

### 1. Find the Vertex:
The formula for the x-coordinate of the vertex is given by:

\[
x = -\frac{b}{2a}
\]

Substituting the values of \( a \) and \( b \):

\[
x = -\frac{-6}{2 \cdot 3} = \frac{6}{6} = 1
\]

Now, substitute \( x = 1 \) into the function to find the y-coordinate of the vertex:

\[
f(1) = 5 - 6(1) + 3(1)^2 = 5 - 6 + 3 = 2
\]

So, the vertex is at \( (1, 2) \).

### 2. Find the Axis of Symmetry:
The axis of symmetry is a vertical line that passes through the vertex. Its equation is:

\[
x = 1
\]

### Summary:
- **Vertex:** \((1, 2)\)
- **Axis of Symmetry:** \(x = 1\)

Would you like more details or have any questions?

Here are some related questions you might find helpful:
1. How do you complete the square to find the vertex form of a quadratic function?
2. What is the effect of changing the coefficient \( a \) on the graph of a quadratic function?
3. How do you determine if a quadratic function opens upwards or downwards?
4. How can you find the y-intercept of a quadratic function?
5. What are the applications of finding the vertex in real-life scenarios?

**Tip:** The vertex represents the maximum or minimum point of a parabola, which can be particularly useful in optimization problems.

State the vertex and axis of symmetry for the function f(x) = 5 - 6x + 3x^2.

Learn how to find the vertex and axis of symmetry for the quadratic function f(x) = 5 - 6x + 3x^2. This step-by-step guide explains key concepts like vertex formula and axis of symmetry, perfect for high school students in Grades 9-12.

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