Subjects algebra

Parabola Properties 971E46

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1. **Problem 1: Analyze the parabola in the first box** 1. The parabola opens upwards, so its concavity is upward. 2. The vertex is at the lowest point of the parabola, near the y-axis. 3. The axis of symmetry is the vertical line through the vertex, which is the y-axis, so $x=0$. 4. The minimum value is the y-coordinate of the vertex since it opens upward. 5. The x-intercepts are the points where the parabola crosses the x-axis, near the left and right of the vertex. 6. The y-intercept is at the vertex, where the parabola crosses the y-axis. 7. The domain of any parabola is all real numbers: $(-\infty, \infty)$. 8. The range is from the y-coordinate of the vertex to positive infinity: $[y_{vertex}, \infty)$. 2. **Problem 2: Analyze the parabola in the second box** 1. The parabola opens upwards, so its concavity is upward. 2. The vertex is near the bottom left quadrant, with negative x and y values. 3. The axis of symmetry is a vertical line through the vertex, so $x = x_{vertex}$. 4. The minimum value is the y-coordinate of the vertex. 5. The x-intercepts are near the left and right sides of the vertex. 6. The y-intercept is below the x-axis. 7. The domain is all real numbers: $(-\infty, \infty)$. 8. The range is from the y-coordinate of the vertex to positive infinity: $[y_{vertex}, \infty)$. **Summary:** Both parabolas open upwards, have vertical axes of symmetry through their vertices, domains of all real numbers, and ranges starting at their minimum y-values (the vertex y-coordinates) extending to infinity.