Answer:
Vertex:
Y-intercept:
Step-by-step explanation:
The x-coordinate of the vertex would be and the y-coordinate of the vertex is whatever the output is given the value of x.
Therefore, the x-coordinate of the vertex is
This means the y-coordinate of the vertex is
So, the vertex is
The y-intercept of a function is the y-value at which x=0, or the y-value when the function crosses the y-axis. Therefore, if we plug x=0 into the function, we see that , so our y-intercept is -8 or (0,-8).
I attached a graph below to help you visualize the vertex and y-intercept given the function.
We have 2 denominators that we need to get rid of. Whenever there are the denominators, all we have to do is multiply all whole equation with the denominators.
Our denominators are both 2 and x+1. Therefore, we multiply the whole equation by 2(x+1)
Then shorten the fractions.
Distribute in all.
We should get like this. Because the polynomial is 2-degree, I'd suggest you to move all terms to one place. Therefore, moving 2x+2 to another side and subtract.
We are almost there. All we have to do is, solving for x by factoring. (Although there are more than just factoring but factoring this polynomial is faster.)
Thus, the answer is x = 3, -2