1. **State the problem:** We are given a parabola with specific points and asked to identify its x-intercepts, y-intercept, vertex, and axis of symmetry. 2. **Identify the x-intercepts:** The x-intercepts are the points where the parabola crosses the x-axis, meaning the y-value is 0. From the problem, these points are given as $(-2, 0)$ and $(5, 0)$. 3. **Identify the y-intercept:** The y-intercept is where the parabola crosses the y-axis, meaning the x-value is 0. We can find it by using the vertex form or by finding the equation of the parabola and evaluating at $x=0$. 4. **Find the equation of the parabola:** The vertex form of a parabola is: $$y = a(x - h)^2 + k$$ where $(h, k)$ is the vertex. Given vertex $(1.5, -9)$, the equation is: $$y = a(x - 1.5)^2 - 9$$ 5. **Use an x-intercept to find $a$:** Using point $(-2, 0)$: $$0 = a(-2 - 1.5)^2 - 9$$ $$0 = a(-3.5)^2 - 9$$ $$0 = a(12.25) - 9$$ $$a(12.25) = 9$$ $$a = \frac{9}{12.25} = \frac{9}{12.25}$$ 6. **Simplify $a$:** $$a = \frac{9}{12.25} = \frac{9}{\cancel{12.25}} = 0.7347$$ (approximate) 7. **Find the y-intercept by evaluating at $x=0$:** $$y = 0.7347(0 - 1.5)^2 - 9$$ $$y = 0.7347(2.25) - 9$$ $$y = 1.653 - 9 = -7.347$$ So the y-intercept is approximately $(0, -7.35)$. 8. **Axis of symmetry:** The axis of symmetry is the vertical line through the vertex: $$x = 1.5$$ **Final answers:** - X-Intercepts: $(-2, 0)$ and $(5, 0)$ - Y-Intercept: $(0, -7.35)$ - Vertex: $(1.5, -9)$ - Axis of Symmetry: $x = 1.5$