5.  Determine the axis of symmetry for the quadratic function y=−x²  + 6x − 8.  *

10 points

x = 2

x = -3

x = 3

x = -2

The axis of symmetry for a quadratic function in the form \( y = ax^2 + bx + c \) can be found using the formula:

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

For the given quadratic function:

\[
y = -x^2 + 6x - 8
\]

Here, \(a = -1\) and \(b = 6\).

Substituting the values into the formula:

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

So, the axis of symmetry is \(x = 3\).

Would you like more details or have any questions? Here are some related questions:

1. How do you find the vertex of a quadratic function?
2. What is the significance of the axis of symmetry in a quadratic graph?
3. How does the sign of the coefficient \(a\) affect the direction of the parabola?
4. How can you find the y-coordinate of the vertex once you have the axis of symmetry?
5. What are the roots of the quadratic function \(y = -x^2 + 6x - 8\)?

**Tip:** The axis of symmetry always passes through the vertex of the parabola, and it divides the parabola into two mirror-image halves.

Learn how to determine the axis of symmetry for the quadratic function y = -x^2 + 6x - 8 with a step-by-step solution. Understand the quadratic formula and axis of symmetry formula application. Suitable for Grades 9-10 students.

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