Final answer:
The y-intercept of the quadratic equation y = -x^2 + 14x - 51 is -51, which is the value of y when x equals 0.
Step-by-step explanation:
When finding the y-intercept of a quadratic equation such as y = -x2 + 14x - 51, you are looking for the point where the graph intersects the y-axis. This occurs when the value of x is 0. Substituting 0 for x in the equation gives us y = -(0)2 + 14(0) - 51, which simplifies to y = -51. Therefore, the y-intercept is -51.