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

Answer:

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

$x= -1 , x= 5$

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

$V_x = -\frac{b}{2a}$

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

$V_x = -\frac{-4}{2*1}= 2$

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

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

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

Step-by-step 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:

$V_x = -\frac{b}{2a}$

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

And replacing we got:

$V_x = -\frac{-4}{2*1}= 2$

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.