Short Answer 
The vertex form of a parabola is expressed as y = a(x Рh)¬≤ + k, with the vertex at (9, -14) leading to the equation y = a(x Р9)¬≤ Р14. We determine that the coefficients a, b, and c, where c = -14, can yield a total of -23 for a + b + c, indicating a specific relationship among the coefficients.
Step 1: Understand the Vertex Form of a Parabola
The equation of a parabola is often expressed in the vertex form: y = a(x Рh)¬≤ + k. Here, (h, k) represents the vertex of the parabola. In our problem, the vertex is given as (9, -14), which allows us to set up the equation as y = a(x Р9)¬≤ Р14.
Step 2: Identify the Coefficients
The equation can be rewritten to emphasize its standard form, y = ax² + bx + c, where we identify the coefficients a, b, and c. In this case, c is -14. Since the parabola intersects the x-axis at two points, the value of a must be negative. This is necessary for the parabola to open downwards, which affects the overall shape of the graph.
Step 3: Calculate the Sum of Coefficients
To find the sum of the coefficients a, b, and c, we simply add them together. The expression we are evaluating is a + b + c, where we know that c = -14. Based on the options presented, we conclude that the potential total for a + b + c could be -23. This indicates a specific relation between the coefficients, leading us to our stated sum.