Find the axis of symmetry and the vertex of the graph of $f\left(x\right)=\frac{2}{5}x^2-4x+14$ .
The axis of symmetry is $x=$ , and the vertex is $\text{(}$  $\text{,}$  $\text{)}$ .

To find the axis of symmetry and the vertex of the quadratic function $ f(x) = \frac{2}{5}x^2 - 4x + 14 $, we can use the following steps:

### Axis of Symmetry
The general form of a quadratic function is:
\[
f(x) = ax^2 + bx + c
\]
where $ a = \frac{2}{5} $, $ b = -4 $, and $ c = 14 $.

The formula for the axis of symmetry is:
\[
x = \frac{-b}{2a}
\]
Substituting the values of $ a $ and $ b $:
\[
x = \frac{-(-4)}{2 \times \frac{2}{5}} = \frac{4}{\frac{4}{5}} = 4 \times \frac{5}{4} = 5
\]
So, the axis of symmetry is $ x = 5 $.

### Vertex
The vertex occurs at the point $ (x, f(x)) $, where $ x $ is the axis of symmetry. So, we substitute $ x = 5 $ into the original function to find the corresponding $ y $-coordinate:
\[
f(5) = \frac{2}{5}(5)^2 - 4(5) + 14 = \frac{2}{5}(25) - 20 + 14 = 10 - 20 + 14 = 4
\]
Thus, the vertex is $ (5, 4) $.

### Final Answer:
- The axis of symmetry is $ x = 5 $.
- The vertex is $ (5, 4) $.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How do you find the y-intercept of a quadratic function?
2. What is the significance of the vertex in the graph of a parabola?
3. How does the coefficient $ a $ in the quadratic function affect the shape of the graph?
4. Can you determine if the vertex is a maximum or a minimum from the function?
5. How can you rewrite the function in vertex form?

**Tip:** The axis of symmetry is always the x-coordinate of the vertex in a quadratic function.

Find the axis of symmetry and the vertex of the graph of $f\left(x\right)=\frac{2}{5}x^2-4x+14$. The axis of symmetry is $x=$ , and the vertex is $( , )$.

Learn how to find the axis of symmetry and vertex of the quadratic function f(x) = (2/5)x^2 - 4x + 14 with a clear step-by-step solution. This problem covers quadratic functions, algebraic formulas, and vertex calculation. Ideal for students in Grades 9-12.

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