Find the axis of symmetry of the given function. f(x)=-2x^2+16x-27

To find the axis of symmetry of the quadratic function:

\[
f(x) = -2x^2 + 16x - 27
\]

We use the formula for the axis of symmetry of a quadratic function \( f(x) = ax^2 + bx + c \), which is given by:

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

In this case:
- \( a = -2 \)
- \( b = 16 \)

Now, substitute these values into the formula:

\[
x = \frac{-16}{2(-2)} = \frac{-16}{-4} = 4
\]

Thus, the axis of symmetry is:

\[
x = 4
\]

Would you like any further details or have any questions?

Here are five related questions you might find helpful:
1. How do you find the vertex of the quadratic function?
2. What is the significance of the axis of symmetry in a parabola?
3. How do you determine whether a quadratic opens upwards or downwards?
4. Can the axis of symmetry be found using factoring or completing the square?
5. How does the discriminant of a quadratic equation relate to its graph?

**Tip:** The axis of symmetry always passes through the vertex of a parabola!

Discover how to find the axis of symmetry for the quadratic function f(x) = -2x^2 + 16x - 27. This problem covers key algebraic concepts and formulas, including the axis of symmetry formula and its relation to parabolas. Suitable for students in Grades 9-11.

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