Question

Which of the following equations best describes a square root function that is reflected across the x-axis and has a vertex of (−4,2)?

A.
`y=√(-(x-4)) +2`

B.
`y= -√(x+2)-4`

C.
`y=-√(x+4) +2`

D.
`y=-√(x-4) +2`

Answer 1

C

Explanation:

Rather than picking, let's try to construct one from the description.

reflected over the x axis means -
`√(x)`

the vertex is usually at (0,0), now how do we move a graph? or in other words translating it.

To move left and right you use
`√(x-h)` where if you subtract h you move right and if you add h you move left. we go from (0,0) to (-4,2). so 0 to -4 is 4 left, so that means we add 4.

To move up and down we use
`√(x)+v` Here if v is positive you move up and if v is negative you move down. going from (0,0) to (-4,2) it moves up 2

So now we put them all together
`-√(x+4)+2` And if you look, C matches that exactly.