How do you write an equation for the parabola with vertex (-1,2) and directrix x=-2?

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How do you write an equation for the parabola with vertex (-1,2) and directrix x=-2?

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Answer 1 · 2018-06-24T15:14:38

We need to know the value of $p$ $p$ in order to write the equation.

Explanation:

Since the vertex is the same distance from both the focus and the directrix, we don't need to know the focus. The vertex is at the x-value of $- 1$ $-1$ and the directrix is 1 unit away at $x = - 2$ $x=-2$ , so $p = 1$ $p=1$ .

Before we go any further, we should know that the directrix is always outside of the parabola. Since it's a vertical line and is to the left of the parabola, the graph opens to the right. Here's the standard form for a right-facing parabola:

$x = \frac{1}{4 p} {(y - k)}^{2} + h$ $x=1/(4p)(y-k)^2+h$

We can use this to find our scale factor. We know that $p = 1$ $p=1$ , so the scale factor is $\frac{1}{4}$ $1/4$ . We can also plug in the values for our vertex to get our equation:

$x = \frac{1}{4} {(y - 2)}^{2} - 1$ $x=1/4(y-2)^2-1$

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How do you write an equation for the parabola with vertex (-1,2) and directrix x=-2?

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Explanation:

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