Question

A) give the vertex and B) axis of symmetry of the graph for the equation given. C) then graph the equation, include a t-chartY= - 1/2|x-1| +3

Answer 1

A) Notice that the given function is the function absolute value translated 1 unit to the right, dilated by a factor of 1/2, reflected over the x-axis, and finally, translated two units up. Therefore

`y=-(1)/(2)|x-1|+3`

has a vertex with coordinates:

`(1,3)\text{.}`

B) Since the vertex is at (1,3), the graph has an axis of symmetry with equation:

`x=1._{}`

C) The t-chart and the graph of the equation are as follows: