Final answer:
The vertex of the quadratic equation y = x^2 - 12x + 40 is found using the vertex formula (-b/2a, f(-b/2a)) which results in the vertex (6, 4).
Step-by-step explanation:
To determine the vertex of the quadratic equation y = x^2 − 12x + 40, we can use the vertex formula for a parabola opening upwards, which is given by the formula (-b/2a, f(-b/2a)) where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c. In the given equation, a = 1 and b = -12.
Applying the vertex formula, we find the x-coordinate of the vertex to be x = -(-12)/(2*1) = 6. To find the y-coordinate of the vertex, we substitute x = 6 back into the equation to get y = (6)^2 - 12(6) + 40 = 36 - 72 + 40 = 4. Therefore, the vertex of the parabola is (6, 4).