A parabola is set of all points in a aircraft which room an equal distance away native a given point and offered line. The point is dubbed the focus that the parabola and also the heat is called the directrix.

The emphasis lies ~ above the axis of the contrary of the parabola.

You are watching: Which equation describes a parabola that opens up or down and whose vertex is at the point (h, v)?

### Finding the emphasis of a parabola provided its equation

If you have actually the equation the a parabola in vertex form y=a(x−h)2+k, climate the vertex is at (h,k) and the focus is (h,k+14a).

Notice that right here we space working v a parabola with a vertical axis of symmetry, so the x-coordinate of the focus is the exact same as the x-coordinate of the vertex.

Example 1:

find the focus of the parabola y=18x2.

Here h=0and k=0, therefore the crest is in ~ the origin. The works with of the emphasis are (h,k+14a) or (0,0+14a).

Since a=18, us have

14a=1(12)

=2

The emphasis is at (0,2).

Example 2:

uncover the emphasis of the parabola y=−(x−3)2−2.

Here h=3 and k=−2, therefore the peak is in ~ (3,−2). The coordinates of the emphasis are (h,k+14a) or (3,−2+14a).

Here a=−1, therefore

−2+14a=−2−14

=−2.25

The focus is at (3,−2.25).

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