Final answer:
The complete function f(x) = 6(1-x) is represented by A) f(x) = 6 - 6x, which is obtained by applying the distributive property. For the nature of f(x) at x=3, y = x² represents a function with a positive value and a slope decreasing in magnitude. The quadratic equation is solved using the quadratic formula derived from the standard form of a quadratic equation.
Step-by-step explanation:
The complete function f(x) = 6(1-x) is represented when expanded out. The distributive property is applied to multiply 6 by each term inside the parentheses.
So the function f(x) would be expanded as:
f(x) = 6 - 6x
Therefore, the answer is A) f(x) = 6 - 6x.
When discussing the nature of f(x) at x=3 with a positive value and slope that is decreasing in magnitude with increasing x, this would correspond to a function where the rate of increase is becoming less steep. Among the given options, y = x² would have this property, since the slope of a quadratic function decreases as x increases from a certain point.
When solving a quadratic equation like x² + 1.2 x 10-2x - 6.0 × 10-3 = 0 or x²+0.0211x-0.0211=0, you typically use the quadratic formula which is derived from the standard form ax² + bx + c = 0. In general, the quadratic formula states that for a quadratic equation of this form, the solutions for x can be found using:
x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation.