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. $y=\sqrt{-(x-4)} +2$

B. $y= -\sqrt{x+2}-4$

C. $y=-\sqrt{x+4} +2$

D. $y=-\sqrt{x-4} +2$

Answer 1

Answer:

C

Step-by-step explanation:

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

reflected over the x axis means -$\sqrt{x}$

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 $\sqrt{x-h}$ 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 $\sqrt{x}+v$ 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 $-\sqrt{x+4}+2$  And if you look, C matches that exactly.