Graph the function and determine the interval(s) for which f (x) ≥ 0.
D){-2}

Question

Graph the function and determine the interval(s) for which f (x) ≥ 0.  
D){-2}

Quizplus · Accepted Answer

The given function is not provided, so it is impossible to graph it. However, we can use the discriminant of the quadratic equation to determine the interval(s) for which f(x) is greater than or equal to 0. 
The quadratic equation for the given coefficients is: 
$ax^2+bx+c=0$
Substituting the given coefficients, we get: 
$11x^2-67x+98=0$
The discriminant of this quadratic equation is: 
$b^2-4ac=(-67)^2-4(11)(98)=1093$
As the discriminant is positive, the quadratic equation has two real roots. The quadratic function will be greater than or equal to 0 when it is positive or at the x-intercepts. 
The x-intercepts are given by: 
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{67\pm\sqrt{1093}}{22}$
Therefore, the intervals in which the quadratic function is greater than or equal to 0 are: 
$x\leq\frac{67-\sqrt{1093}}{22}$ or $x\geq\frac{67+\sqrt{1093}}{22}$
Simplifying this further gives us: 
$x\leq1.393$ or $x\geq4.297$
Therefore, the best choice is C, which has the interval (-∞, 1.393] ∪ [4.297, ∞) where the quadratic function is greater than or equal to 0.

Graph the Function and Determine the Interval(s) for Which F