how to find the axis of symmetry: y= x²-9

To find the axis of symmetry for a quadratic function of the form \( y = ax^2 + bx + c \), you can use the formula for the x-coordinate of the axis of symmetry:

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

For the given equation \( y = x^2 - 9 \), let's compare it with the general quadratic form \( y = ax^2 + bx + c \):

- \( a = 1 \)
- \( b = 0 \)
- \( c = -9 \)

Using the formula for the axis of symmetry:

\[
x = \frac{-b}{2a} = \frac{-0}{2(1)} = 0
\]

So, the axis of symmetry is the vertical line \( x = 0 \).

Would you like more details or have any other questions?

Here are 5 related questions:
1. How do you find the vertex of a parabola?
2. What is the significance of the axis of symmetry in graphing parabolas?
3. How does changing the value of \( a \) affect the axis of symmetry?
4. Can a quadratic function have a horizontal axis of symmetry?
5. How would the axis of symmetry change if \( b \neq 0 \)?

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

Learn how to find the axis of symmetry for the quadratic equation y = x² - 9. This solution explains the axis of symmetry formula x = -b / 2a, highlights algebraic concepts, and is suitable for students in Grades 9-10.

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