How do i find the vertex of this equation/inequality? f(x)> -2|x-5|+4

The vertex of the inequality is (5, 4)

Step-by-step explanation:

The vertex of the equation would be at (0,0) before the translations.

Move the vertex 5 to the right because of the -5 in the absolute value. (5, 0)

The -2 would not affect the vertex, only the direction and slope.

Move the vertex 4 upwards because of the + 4 at the end. (5, 4)

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source: