Final answer:
To correct the error, we need to find the correct vertex of the function y = -4.5x^2 - 47.5x + 63. The correct vertex is (5.28, -123.98).
Step-by-step explanation:
The student has incorrectly found the vertex for the function y = -4.5x^2 - 47.5x + 63. To correct the error, we need to find the correct vertex. The vertex of a quadratic function in the form y = ax^2 + bx + c can be found using the formula x = -b / (2a) and then substituting the value of x into the equation to find the y-coordinate.
In this case, a = -4.5, b = -47.5, and c = 63. Plugging these values into the formula x = -b / (2a), we get x = -(-47.5) / (2 * -4.5) = 5.28 (rounded to two decimal places). Substituting x = 5.28 into the equation, we get y = -4.5(5.28)^2 - 47.5(5.28) + 63 = -123.98 (rounded to two decimal places).
Therefore, the correct vertex of the function y = -4.5x^2 - 47.5x + 63 is (5.28, -123.98).