+1995 What are the coordinates of the hole in the graph of the function?
f(x)=5x−20 / 2x2−5x−12
Enter your answer by filling in the boxes. Enter your answer as simplified fractions, as necessary.
hole: ( 4 , 20/11 )
was kind of confused on what to do with the 5 so it may not be 20, im unsure.
+129852 5x -20 5 ( x-4) 5
____________ = ____________ = _______ (1)
2x^2 - 5x - 12 (x - 4) (2x + 3) 2x + 3
Note that since (x - 4) is a factor in the numerator, we might guess that it is also a factor in the denominator.....knowing this....the denominator should be easy to factor
The hole occurs where x - 4 = 0 ⇒ at x = 4
To find the y coordinate , sub 4 back into (1) ⇒ 5 5
________ = _____
2(4) + 3 11
So......the hole occurs at (4, 5/11)
See the graph here : https://www.desmos.com/calculator/uf623od70z
