find the vertex and axis of symmetry y=(x-2)^2-3

The given quadratic function is:

\[
y = (x - 2)^2 - 3
\]

This is already in **vertex form** of a quadratic equation, which is generally:

\[
y = a(x - h)^2 + k
\]

Where:
- \((h, k)\) is the vertex of the parabola.
- The axis of symmetry is the vertical line \(x = h\).

For the equation \(y = (x - 2)^2 - 3\):
- \(h = 2\)
- \(k = -3\)

Thus:
- The **vertex** is \((2, -3)\).
- The **axis of symmetry** is the vertical line \(x = 2\).

### Summary:
- **Vertex**: \((2, -3)\)
- **Axis of symmetry**: \(x = 2\)

Do you want more details or have any questions?

### Related Questions:
1. How do you determine if the parabola opens upwards or downwards?
2. What is the significance of the vertex in a quadratic equation?
3. How would you rewrite a quadratic equation in vertex form from standard form?
4. How do you find the x-intercepts of this parabola?
5. Can you find the minimum or maximum value of the quadratic function?

### Tip:
In a quadratic function in vertex form, the sign of \(a\) (the coefficient of \((x-h)^2\)) determines if the parabola opens upwards (if \(a > 0\)) or downwards (if \(a < 0\)).

Find the vertex and axis of symmetry y = (x - 2)^2 - 3

Learn how to find the vertex and axis of symmetry for the quadratic function y = (x - 2)^2 - 3. This example demonstrates the use of the vertex form of a quadratic equation and identifies the parabola's key features. Suitable for students in Grades 8-10.

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