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?

---

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.