Final answer:
The zeros of the quadratic function f(x) = x^2 + 8x + 13, when rounded to the nearest hundredth, are -2.27 and -5.73, found using the quadratic formula.
Step-by-step explanation:
To find the zeros of the quadratic function f(x) = x2 + 8x + 13, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a). For our equation, a = 1, b = 8, and c = 13. Applying these values to the quadratic formula, we get:
x = (-8 ± √((82) - 4(1)(13)))/(2(1))
x = (-8 ± √(64 - 52))/2
x = (-8 ± √(12))/2
The square root of 12 is approximately 3.46, rounded to the hundredth. Therefore, we have:
x = (-8 ± 3.46)/2
This results in two possible solutions for x. These are:
- x = (-8 + 3.46)/2 ≈ -2.27
- x = (-8 - 3.46)/2 ≈ -5.73
Thus, the zeros of the function rounded to the nearest hundredth are -2.27 and -5.73.