Where does f(x) = 3x2 – 11x – 4 intersect the x-axis?

Answer:The x-intercepts are (4,0) and (-1/3,0).Step-by-step explanation:f or any relation/function will intersect the x-axis when y is 0.Set that's what we will do is set y to 0 and solve for x.0=3x^2-11x-4I'm going to attempt to factor.a=3b=-11c=-4We need to find two numbers that multiply to be ac and add up to be b.ac=-12=-12(1)b=-11=-12+1Let's factor 3x^2-11x-4 by grouping.3x^2-11x-43x^2-12x+1x-4       ; I replaced -11x with -12x+1xGroup the first 2 pairs and group the last two pairs like so:(3x^2-12x)+(1x-4)Now factor what you can from each pair:3x(x-4)+1(x-4)Now you have two terms, both with the common factor (x-4) so factor it out:(x-4)(3x+1)Now let's go back to solving:3x^2-11x-4=0This is the same as solving:(x-4)(3x+1)=0  (because this is just the factored form of the original equation.)Now this means either x-4=0 or 3x+1=0.We need to solve both.x-4=0 can be solved by adding 4 on both sides resulting in x=4.3x+1=0 requires two steps.3x+1=0Subtract 1 on both sides:3x=-1Divide both sides by 3:x=-1/3The x-intercepts are (4,0) and (-1/3,0).