Answer:
Step-by-step explanation:
To find the leftmost x-intercept of the function f(x) = 3x^2 - 15x - 6, we need to set the function equal to zero and solve for x.
Given that the function is f(x) = 3x^2 - 15x - 6, we need to find the x-intercepts, where the function crosses the x-axis.
Set f(x) = 0:
3x^2 - 15x - 6 = 0
Now, we can solve for x using the quadratic formula:
x = (-(-15) ± sqrt((-15)^2 - 4*3*(-6)))/(2*3)
x = (15 ± sqrt(225 + 72))/6
x = (15 ± sqrt(297))/6
x = (15 ± sqrt(3*99))/6
x = (15 ± 3*sqrt(11))/6
x = 5 ± sqrt(11)/2
The x-intercepts are at x = 5 + sqrt(11)/2 and x = 5 - sqrt(11)/2. Since we are looking for the leftmost x-intercept, we take x = 5 - sqrt(11)/2 as the answer.
Therefore, the leftmost x-intercept of the function f(x) = 3x^2 - 15x - 6 is approximately -0.821 (rounded to the nearest thousandth).
