To find the zeroes of the quadratic function f(x) = x2 + 6x + 8, we need to determine the values of x that make the function equal to zero. This can be done using the quadratic formula, factored form, or completing the square. In this case, we will factor the expression.
The first step in factoring is to write f(x) in the standard format:
f(x) = x2 + 6x + 8
Next, we need to find two numbers that multiply to the constant term (8) and add up to the coefficient of x (6). The numbers that satisfy these conditions are 2 and 4, since:
- 2 × 4 = 8
- 2 + 4 = 6
Thus, we can factor the quadratic as:
f(x) = (x + 2)(x + 4)
To find the zeroes, we set f(x) = 0:
(x + 2)(x + 4) = 0
This equation holds true if either factor equals zero, so we solve each one:
- x + 2 = 0 → x = -2
- x + 4 = 0 → x = -4
Therefore, the zeroes of the function f(x) = x2 + 6x + 8 are x = -2 and x = -4.
In summary, the function intersects the x-axis at the points (−2, 0) and (−4, 0).