Question

A parabola opens to the left. Which could be the equation of the parabola?

(x – 4)2 = 4(y + 3)
(x – 4)2 = –4(y + 3)
(y – 4)2 = 4(x + 3)
(y – 4)2 = –4(x + 3)

Answer 1

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

Explanation:

When parabola opens the left then it is a horizontal parabola

Vertex form of horizontal parabola is

`(y-k)^2= 4p(x-h)`

where (h,k) is the vertex

When the parabola opens to the right then 4p is positive

when parabola opens to the left then 4p is negative

Now we look at the given equation and check with vertex form of parabola

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

Here the value of 4p is negative , so parabola opens left