Answer:
The quadratic equation or function represented by the given information has a vertex at (-1/2, -25/4), a y-intercept at (0, -6), an axis of symmetry at x = -1/2, x-intercepts at (-3, 0) and (2, 0), and opens upwards.
Step-by-step explanation:
Based on the given information, the following characteristics can be identified for the quadratic equation or function:
1. Vertex: The vertex of the parabola is located at (-1/2, -25/4). This means that the parabola is symmetric and opens either upwards or downwards.
2. Y-intercept: The y-intercept of the parabola is at the point (0, -6). This means that the parabola intersects the y-axis at this point.
3. Axis of symmetry: The axis of symmetry of the parabola is the vertical line x = -1/2. This line divides the parabola into two symmetrical halves.
4. Roots or x-intercepts: The parabola intersects the x-axis at the points (-3, 0) and (2, 0). These are the values of x where the parabola intersects the x-axis, also known as the roots or x-intercepts.
5. Opening: The given information states that the parabola opens upwards. This means that the coefficient of the leading term (the x^2 term) in the quadratic equation is positive.