Question

Which graph represents the equation y² = –4x?

Answer 1

the first graph x=1 if it's not correct tell me

Answer 2

The 1st graph represents the given equation.

Explanation:

We are given the equation
`y^2=-4x`

Now, as we know,

If in the equation of a parabola 'y' is squared, then the parabola opens left or right.

So, the given parabola opens left or right. ............(1)

If in the equation of a parabola
`y^2=4ax`, the value of 'a' is negative, then the parabola opens downwards or left.

Since, in the given parabola, value of 'a' is -1.

So, the parabola opens downwards or right. ...........(2)

Hence, from (1) and (2), we get,

The parabola
`y^2=-4x` opens to the left.

Moreover, the focus of the parabola
`(y-k)^2=4p(x-h)` is (h+p,k) and the directrix is x= -p

So, the focus of
`y^2=-4x` is (0-1,0) i.e. (-1,0) and the directrix is x= 1.

So, the 1st graph represents the given equation.