Determine the zeros of the quadratic function y=−x2+16x−39 . (When listing the smaller zero, remember that negative values are always smaller than positive values.)(1 point) smaller zero: x= ; greater zero: x=
To find the zeros of a quadratic function, we set the function equal to zero and solve for x. So, we have:
- x^2 + 16x - 39 = 0
To factor this quadratic equation, we look for two numbers whose sum is 16 and whose product is -39. After some trial and error, we find that 13 and -3 fit these conditions. Thus, we can rewrite the equation as:
(x - 13)(x + 3) = 0
Setting each factor equal to zero, we have:
x - 13 = 0 --> x = 13
x + 3 = 0 --> x = -3
Therefore, the smaller zero is x = -3 and the greater zero is x = 13.