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-4
I'm going to attempt to factor.
a=3
b=-11
c=-4
We need to find two numbers that multiply to be ac and add up to be b.
ac=-12=-12(1)
b=-11=-12+1
Let's factor 3x^2-11x-4 by grouping.
3x^2-11x-4
3x^2-12x+1x-4 ; I replaced -11x with -12x+1x
Group 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=0
This 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=0
Subtract 1 on both sides:
3x=-1
Divide both sides by 3:
x=-1/3
The x-intercepts are (4,0) and (-1/3,0).
