For each equation give the vertex of the graph y x32 5 verte

For each equation give the vertex of the graph. y =(x-3)^2 +5 vertex: y =|x|-2 vertex: y = |x + 5| - 2 vertex: y = x^2 vertex: y=|x + 8|-12 vertex:

Solution

a) y = (x-3)^2 + 5

standard equation in vertex form is given by

y = a ( x-h)^2 + k

where h , k are the vertex

so vertex is ( 3,5 )

b) y = | x| - 2

standrad equation is

y = a | x- h | + k

vertex is ( 0 , -2 )

c) y = | x + 5 | - 2

vertex is ( -5 , -2 )

d) y = x^2

vertex is (0,0)

e) y = | x + 8 | - 12

vertex is ( -8 , -12 )