The given function is:

\[
f(x) = x^2 - 3x - 4
\]

This is a quadratic function, and it can be analyzed in several ways.

### Key Properties:
1. **Vertex**: The vertex of a quadratic function \( f(x) = ax^2 + bx + c \) is given by the formula:
   \[
   x_{\text{vertex}} = -\frac{b}{2a}
   \]
   For \( f(x) = x^2 - 3x - 4 \), \( a = 1 \), \( b = -3 \), and \( c = -4 \), so the \( x \)-coordinate of the vertex is:
   \[
   x_{\text{vertex}} = -\frac{-3}{2(1)} = \frac{3}{2}
   \]
   To find the \( y \)-coordinate of the vertex, substitute \( x = \frac{3}{2} \) back into the function:
   \[
   f\left(\frac{3}{2}\right) = \left(\frac{3}{2}\right)^2 - 3\left(\frac{3}{2}\right) - 4 = \frac{9}{4} - \frac{9}{2} - 4 = -\frac{25}{4}
   \]
   Thus, the vertex is \( \left(\frac{3}{2}, -\frac{25}{4}\right) \).

2. **Axis of Symmetry**: The axis of symmetry is the vertical line that passes through the vertex. It is:
   \[
   x = \frac{3}{2}
   \]

3. **Y-intercept**: The y-intercept occurs when \( x = 0 \). Substitute

Explore the properties of the quadratic function f(x) = x^2 - 3x - 4. This solution provides a step-by-step analysis, including vertex calculation, axis of symmetry, and y-intercept. Perfect for students in Grades 9-11.

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