Let's analyze and answer each part of the problem based on the graph of the parabola.

(a) Direction of the Parabola

The parabola in the graph opens upward. We know this because the arms of the parabola extend upward as we move away from the vertex.

Answer for (a): Upward

(b) Intercepts

1. x-intercepts: The points where the graph crosses the x-axis.

   • Based on the graph, the x-intercepts appear to be at approximately $(-5, 0)$ and $(1, 0)$.

   Answer for x-intercepts: $(-5, 0), (1, 0)$

2. y-intercept: The point where the graph crosses the y-axis.

   • Observing the graph, the y-intercept is at $(0, -5)$.

   Answer for y-intercept: $(0, -5)$

(c) Vertex

The vertex of the parabola is the lowest point on the graph, given it opens upward.

• The vertex is located at approximately $(-2, -9)$.

Answer for (c): Vertex: $(-2, -9)$

(d) Axis of Symmetry

The axis of symmetry is the vertical line that passes through the vertex of the parabola.

• Since the vertex is at $(-2, -9)$, the axis of symmetry is the line $x = -2$.

Answer for (d): Axis of Symmetry: $x = -2$

Would you like a detailed explanation for each part? Here are some additional questions to deepen understanding:

1. What is the standard form equation of a parabola that opens upward or downward?
2. How can we find the vertex of a parabola given its equation in standard form?
3. What role does the axis of symmetry play in the symmetry of a parabola?
4. How can we determine the direction of a parabola based on its equation?
5. What other information can we infer from the vertex and intercepts of a parabola?

Tip: For a quadratic function $y = ax^2 + bx + c$, if $a > 0$, the parabola opens upward; if $a < 0$, it opens downward.