Question

The directress of a parabola is represented by the linear equation y=2, and its vertex is located at (3,1).Both of these attributes of the parabola are graphed below. which of the following is the equation that represents this parabola?

Answer 1

The directrix of the parabola is at y = 2 and its vertex is at (-3,1). Since the directrix is below the vertex, we can say that the parabola will open downwards. The general form to find the equation of the parabola given the directrix and vertex is

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

The value of h for the problem is -3 while the value of k for the problem is 1. Substitute it on the equation above, we get

`\begin{gathered} y=-(x-(-3))^2+1 \\ y=-(x+3)^2+1 \end{gathered}`

Hence, the answer to this problem is option 2. Note that the equation started in a negative sign because the parabola opens downwards.