From the graph provided:

Part (a): Find the x-intercepts

The x-intercepts are the points where the parabola crosses the x-axis. From the graph:

• X-intercepts are $x = -3$ and $x = 1$.

Part (b): Identify another point on the graph

From the graph, another point given is the vertex: $(x, y) = (-1, 8)$.

Part (c): Solve for $a$ and write the equation in factored form

The equation in factored form is: $y = a(x + 3)(x - 1)$ Substitute the vertex point $(-1, 8)$ into the equation to solve for $a$: $8 = a(-1 + 3)(-1 - 1)$ $8 = a(2)(-2)$ $8 = -4a$ $a = -2$

Thus, the equation is: $y = -2(x + 3)(x - 1)$

Would you like further clarifications or details on this process?
Here are five related questions:

1. How do you identify the vertex from a quadratic equation in standard form?
2. What does the value of $a$ tell us about the parabola’s direction?
3. How do you convert factored form to standard form?
4. Can the x-intercepts help verify the accuracy of the equation?
5. What is the importance of symmetry in determining points on the parabola?

Tip: Always verify the equation by substituting multiple points from the graph!