Determine the zeros of the quadratic function y = -x^2 + 16x - 39.(When listing the smaller zero, remember that negative values are always smaller than positive values)
To find the zeros of the quadratic function, we need to set y to zero and solve for x.
0 = -x^2 + 16x - 39
To simplify this quadratic equation, we can multiply through by -1 to make the coefficient of x^2 positive:
0 = x^2 - 16x + 39
Now, we can factor the quadratic equation:
0 = (x - 3)(x - 13)
Setting each factor equal to zero:
x - 3 = 0 or x - 13 = 0
Solving for x in each equation:
x = 3 or x = 13
Therefore, the zeros of the quadratic function y = -x^2 + 16x - 39 are x = 3 and x = 13. The smaller zero is x = 3.