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 $a < 0$).