Question

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

Answer 1

Answer:

Option D.

Step-by-step 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.