The equation you're working with is \( y = (x - 5)^2 - 4 \). This represents a quadratic function, which graphs as a parabola. Let's break it down and then plot the graph:

1. **Vertex Form**: 
   The equation \( y = (x - 5)^2 - 4 \) is already in vertex form, \( y = a(x - h)^2 + k \), where \( (h, k) \) is the vertex of the parabola. Here:
   - \( h = 5 \)
   - \( k = -4 \)

   So, the vertex is at \( (5, -4) \).

2. **Direction**: 
   Since the coefficient of \( (x - 5)^2 \) is positive (it's implicitly 1), the parabola opens **upward**.

3. **Axis of Symmetry**:
   The axis of symmetry is the vertical line \( x = 5 \), which passes through the vertex.

4. **Y-intercept**:
   To find the y-intercept, substitute \( x = 0 \) into the equation:
   \[
   y = (0 - 5)^2 - 4 = 25 - 4 = 21
   \]
   So, the y-intercept is \( (0, 21) \).

5. **Graph**:
   - The parabola has its vertex at \( (5, -4) \).
   - It opens upward and is symmetric about the line \( x = 5 \).
   - A point of interest is \( (0, 21) \), the y-intercept.
   
Would you like me to plot this graph for you?

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**Relative questions:**
1. How would the graph change if the vertex was moved to \( (2, -4) \)?
2. What happens if the parabola opens downward (negative coefficient)?
3. Can you find the x-intercepts of this parabola?
4. What does the axis of symmetry represent in a quadratic graph?
5. How would a different constant affect the vertical shift of the parabola?

**Tip:** The vertex form of a quadratic equation is useful for identifying the vertex and direction of a parabola easily.

Learn how to graph the quadratic equation y = (x – 5)^2 – 4, identify the vertex, axis of symmetry, and y-intercept. This problem highlights key algebraic concepts for Grades 9-11 students.

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