Let's go over the problem step by step based on the image provided.

(a) Does the parabola open upward or downward?

From the graph, the parabola has a "U" shape, which means it opens upward.

• Answer for (a): The parabola opens upward.

(b) Find the intercept(s).

1. Y-intercept: The y-intercept occurs where the graph crosses the y-axis (where $x = 0$). From the graph, it seems that the y-intercept is at the point $(0, 1)$.
2. X-intercepts: The x-intercepts are the points where the graph crosses the x-axis (where $y = 0$). From the graph, it looks like the x-intercepts are approximately at points $x = -1$ and $x = 1$.

• Answer for (b):
  • X-intercepts: $(-1, 0)$, $(1, 0)$
  • Y-intercept: $(0, 1)$

Would you like more details on these solutions or any further explanations?

5 Related Questions:

1. What is the vertex of this parabola, and how does it relate to its direction?
2. How can you find the axis of symmetry of the parabola from the graph?
3. How can you confirm the x-intercepts algebraically if the equation of the parabola is given?
4. What is the general form of a quadratic equation, and how can you use it to find intercepts?
5. How do you determine if a parabola has real or imaginary x-intercepts from its discriminant?

Tip:

When a parabola opens upward, its vertex is the lowest point, and the parabola will have a minimum value.