Question

The vertex of this parabola is at (4,-3). Which of the following could be its

equation?
A. x==3(y - 3)2 + 4
B. X=-3(+4)2-3
C. X=-3(-4) 2-3
D. X=-3(y + 3) - 4

Answer 1

Option D.

Explanation:

From the given graph it is clear that it is a parabola along to the x-axis.

Vertex form of a parabola along the x-axis is

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

where, (h,k) is vertex.

From the graph it is clear that the vertex of the parabola is (4,-3). So, substitute h=4 and k=-3 in the above equation.

`x=a(y-(-3))^2+(4)`

`x=a(y+3)^2+4` ...(1)

The graph passing through (1,-2), so substitute x=1 and y=-2 in the above equation.

`1=a(-2+3)^2+4`

`1-4=a(1)^2`

`-3=a(1)^2`

Substitute a=-3 in equation (1).

`x=-3(y+3)^2+4`

Therefore, the correct option is D.