Final answer:
Without seeing the graph, we can't be certain of the coefficients' signs, but understanding quadratic properties helps us infer that if a > 0, the graph opens up, b > 0 suggests an increasing graph from the y-axis, and c > 0 indicates a positive y-intercept. An example given with specific coefficients suggests option C, though it can't apply universally without the graph.
Step-by-step explanation:
To determine the correct statement about the coefficients of the quadratic function f(x) = ax² + bx + c, we need to analyze the given information and apply our understanding of the properties of quadratic functions. The signs of the coefficients a, b, and c affect the graph's direction, shape, and position on the coordinate plane.
Based on the reference information provided:
- If a > 0, the graph of the quadratic function opens upwards, resembling a 'U' shape.
- If b > 0, the slope of the tangent to the vertex point of the parabola is positive, indicating that the graph initially increases as it moves right from the y-axis.
- If b < 0, the slope of the tangent to the vertex point of the parabola is negative, which means that the graph initially decreases as it moves right from the y-axis.
- If c > 0, the y-intercept of the graph is positive, placing it above the x-axis.
- If c < 0, the y-intercept of the graph is negative, placing it below the x-axis.
Without viewing the graph, you would not be able to definitively determine the correct statement. However, using the reference example of a quadratic equation at² + bt + c = 0 with constants a = 4.90, b = -14.3, and c = -20.0, its graph would open upwards (since a > 0), start with a negative slope (since b < 0), and have a negative y-intercept (since c < 0), which would correspond to option C (a > 0, b < 0, c < 0). However, this example is provided for conceptual understanding and may not reflect the specific graph in question.