Given the equation y = x^2 - 16x + 89 with zeros of x = 8 - 5i and x = 8 +5i, which of the following identifies the general shape of its associated graph?

Answer 1

The equation you provided, \( y = x^2 - 16x + 89 \), is a quadratic equation, which is in the standard form \( y = ax^2 + bx + c \). The general shape of the graph of a quadratic equation is a parabola.

In this case, since the coefficient of \( x^2 \) (which is \( a = 1 \)) is positive, the parabola opens upwards.

Additionally, since the equation has complex zeros (8 - 5i and 8 + 5i), it means that the graph of the function does not intersect the x-axis. Therefore, the parabola is situated entirely above the x-axis.

To summarize, the general shape of the graph associated with the given quadratic equation is an upward-opening parabola that does not intersect the x-axis.