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To find the equation of the axis of symmetry and the coordinates of the vertex for the function given:

\[
y = x^2 - 4x - 3
\]

### 1. Equation of the Axis of Symmetry
For a quadratic function in the form \( y = ax^2 + bx + c \), the axis of symmetry can be found using the formula:
\[
x = -\frac{b}{2a}
\]
In this case:
- \( a = 1 \)
- \( b = -4 \)

Substitute these values into the formula:
\[
x = -\frac{-4}{2 \times 1} = \frac{4}{2} = 2
\]

So, the equation of the axis of symmetry is:
\[
x = 2
\]

### 2. Coordinates of the Vertex
The vertex lies on the axis of symmetry. To find the y-coordinate, substitute \( x = 2 \) back into the equation:

\[
y = (2)^2 - 4 \cdot 2 - 3
\]
\[
y = 4 - 8 - 3 = -7
\]

Thus, the coordinates of the vertex are:
\[
(2, -7)
\]

**Final Answer:**
- The equation of the axis of symmetry is \( x = 2 \).
- The coordinates of the vertex are \( (2, -7) \).

Would you like further details or have any other questions?

Here are some related questions you might consider:
1. How would the vertex change if the equation were \( y = x^2 + 4x - 3 \)?
2. What is the axis of symmetry for the function \( y = 2x^2 - 4x - 3 \)?
3. How can you tell the direction of the parabola's opening from the equation \( y = x^2 - 4x - 3 \)?
4. How would you find the y-intercept of \( y = x^2 - 4x - 3 \)?
5. What effect does changing the constant term have on the vertex?

**Tip:** The vertex formula is a quick way to find the maximum or minimum point of a parabola without graphing.

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = x^2 - 4x - 3. What is the equation of the axis of symmetry?

Step-by-step solution to find the axis of symmetry and the vertex for the quadratic function y = x^2 - 4x - 3. This covers key algebraic concepts, formulas, and theorems in quadratic functions, ideal for students in Grades 8-10.

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