Final answer:
The equation for a quadratic function that opens downward and has a vertex at (3.2, 4.7) is y = -ax^2 + bx + c. Substituting the vertex coordinates into the equation allows us to find the values of a, b, and c.
Step-by-step explanation:
A quadratic function is represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. Since the graph opens downward and has a vertex at (3.2, 4.7), the value of a must be negative in order for the graph to open downward.
The equation for the given quadratic function is therefore y = -ax^2 + bx + c. To find the values of a, b, and c, we can substitute the coordinates of the vertex into the equation.
Substituting (3.2, 4.7) into the equation, we get 4.7 = -a(3.2)^2 + b(3.2) + c. Since the vertex lies on the graph of the quadratic function, this equation must be true.
Solving this equation will give us the values of a, b, and c for the given quadratic function.