Question

Which direction does the parabola x=-9y^(2)+6 open?

Answer 1

The parabola represented by the equation

`x=-9y^2+6`

opens to the left because the coefficient of the

`y^2`

term is negative.

Step-by-step explanation:

The equation you've provided,

`x=-9y^2+6`

, represents a parabola. To determine which direction this parabola opens, look at the coefficient of the

`y^2`

term. In this case, the coefficient is -9, which is negative. This means that the parabola opens to the left if you're looking at a standard graph with x and y axes. In the standard orientation, parabolas that are functions of y² open either left or right depending on the sign of the coefficient before the y² term. If the coefficient is negative as it is in this case, the parabola opens to the left. If it were positive, the parabola would open to the right.