Question

Graph the function f(x) = (x + 1)(x – 5). Use the drop-down menus to complete the steps needed to graph the function

Answer 1

`0 = (x+1)(x-5)`

`x= -1 , x= 5`

`f(x) = x^2 -4x -5`

`V_x = -(b)/(2a)`

With
`a = 1, b=-4 , c=-5`

`V_x = -(-4)/(2*1)= 2`

`f(2) = 2^2 -4*2 -5 = -9`

`f(0) = 0^2 -4*0 -5=-5`

So then the x intercept would be (0,-5). And finally we can graph the function as we can see in the figure attached.

Explanation:

For this case we know the following function:

`f(x) = (x+1)(x-5)`

We can begin the zeros or the values where the function is 0 like this:

`0 = (x+1)(x-5)`

And solving for x we got:

`x= -1 , x= 5`

Now we can rewrite the expression like this:

`f(x) = x^2 -4x -5`

And we can find the position for the vertex at x with this formula:

`V_x = -(b)/(2a)`

With
`a = 1, b=-4 , c=-5`

And replacing we got:

`V_x = -(-4)/(2*1)= 2`

And then with the coordinate of x for the vertex we can find the coordinate of y replacing the value of x obtained for the vertex.

`f(2) = 2^2 -4*2 -5 = -9`

Then we can find the intercept using the value of x=0 and replacing into the function we got:

`f(0) = 0^2 -4*0 -5=-5`

So then the x intercept would be (0,-5). And finally we can graph the function as we can see in the figure attached.