1. **Problem:** Graph the function $$y = (x - 2)^2 - 4$$ and label important features. 2. **Formula and rules:** This is a quadratic function in vertex form $$y = a(x-h)^2 + k$$ where the vertex is at $$(h, k)$$. 3. **Identify vertex:** Here, $a=1$, $h=2$, and $k=-4$, so the vertex is at $$(2, -4)$$. 4. **Axis of symmetry:** The vertical line through the vertex is $$x = 2$$. 5. **Find y-intercept:** Set $$x=0$$: $$y = (0 - 2)^2 - 4 = 4 - 4 = 0$$ So the y-intercept is $$(0, 0)$$. 6. **Find x-intercepts:** Set $$y=0$$: $$0 = (x - 2)^2 - 4$$ $$ (x - 2)^2 = 4$$ $$x - 2 = \pm 2$$ $$x = 2 \pm 2$$ So, $$x=0$$ or $$x=4$$, giving intercepts $$(0,0)$$ and $$(4,0)$$. 7. **Plot points:** Vertex at $$(2,-4)$$, intercepts at $$(0,0)$$ and $$(4,0)$$. 8. **Shape:** Since $$a=1>0$$, the parabola opens upwards. --- **Final answer:** The graph is a parabola with vertex at $$(2,-4)$$, axis of symmetry $$x=2$$, y-intercept $$(0,0)$$, and x-intercepts $$(0,0)$$ and $$(4,0)$$. --- "slug": "parabola graph", "subject": "algebra", "desmos": { "latex": "y=(x-2)^2-4", "features": { "intercepts": true, "extrema": true } }, "q_count": 3