1. **State the problem:** We need to find the vertex, axis of symmetry, and y-intercept of a parabola. 2. **Given information:** The vertex is at $(2, -1)$. 3. **Axis of symmetry:** The axis of symmetry of a parabola is a vertical line passing through the vertex. Since the vertex is at $x=2$, the axis of symmetry is: $$x=2$$ 4. **Y-intercept:** The y-intercept is the point where the graph crosses the y-axis, i.e., where $x=0$. 5. **Find the y-intercept:** Using the vertex form of a parabola: $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. Here, $h=2$ and $k=-1$. 6. **Find $a$ using the y-intercept:** The parabola crosses the y-axis at approximately $y=3$ when $x=0$. Substitute $x=0$, $y=3$: $$3 = a(0 - 2)^2 - 1$$ $$3 = a(4) - 1$$ $$3 + 1 = 4a$$ $$4 = 4a$$ $$a = 1$$ 7. **Equation of the parabola:** $$y = 1(x - 2)^2 - 1 = (x - 2)^2 - 1$$ 8. **Confirm y-intercept:** Substitute $x=0$: $$y = (0 - 2)^2 - 1 = 4 - 1 = 3$$ So the y-intercept is $(0, 3)$. **Final answers:** - Vertex: $(2, -1)$ - Axis of symmetry: $x=2$ - Y-intercept: $(0, 3)$