Respuesta :
x = 0 and x = 4
To find intersection equate them.
x² - 2x - 4 = 2x - 4
subtract 2x - 4 from both sides
x² - 4x = 0 → (take out common factor x)
x(x - 4 ) = 0 ⇒ x = 0 , x = 4
Answer:
[tex]x=0,4[/tex].
Step-by-step explanation:
We have been given two functions.[tex]f(x) = x^2-2x-4[/tex] and [tex]g(x) = 2x - 4[/tex]. We are asked to find the point, where both functions intersect.
To find the intersection point of both graphs, we will equate both equations as:
[tex]x^2-2x-4=2x-4[/tex]
Combine like terms:
[tex]x^2-2x-2x-4+4=2x-2x-4+4[/tex]
[tex]x^2-4x=0[/tex]
Now, we will factor out x as:
[tex]x(x-4)=0[/tex]
Using zero product property, we will get:
[tex]x=0\text{ (or) }x-4=0[/tex]
[tex]x=0\text{ (or) }x=4[/tex]
Therefore, the both graphs intersect at [tex]x=0,4[/tex].
