Subjects algebra

Parabola Properties 51F5Af

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1. **Problem Statement:** Given a parabola that opens upward, crosses the x-axis near -5 and -3, has a vertex near (-4, -9), and does not cross the y-axis. 2. **Determine if the parabola opens upward or downward:** The problem states it opens upward. 3. **Find the intercepts:** - **x-intercepts:** Points where the parabola crosses the x-axis, approximately at $x = -5$ and $x = -3$. - **y-intercept:** The parabola does not cross the y-axis, so there is no y-intercept. 4. **Find the vertex coordinates:** The vertex is given approximately as $(-4, -9)$. 5. **Find the equation of the axis of symmetry:** The axis of symmetry is a vertical line passing through the vertex's x-coordinate, so the equation is $x = -4$. **Final answers:** - Parabola opens: upward - x-intercepts: $-5, -3$ - y-intercept: None - Vertex: $(-4, -9)$ - Axis of symmetry: $x = -4$