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soldier1979 [14.2K]
3 years ago
5

Using the given information, give the vertex form equation for each parabola.

Mathematics
1 answer:
ollegr [7]3 years ago
3 0

Answer:

Step-by-step explanation:

If you plot this point and the directrix on a coordinate plane, you can see that the directrix is 1/4 of a unit below the vertex.  Since, by nature, a parabola opens in the direction opposite the directrix and "hugs" the focus, this is a positive x-squared parabola (meaning it opens upwards).  The formula for this type of a parabola is, in vertex form,

4p(y-k)=(x-h)^2

where p is distance (in units) between the vertex and the directrix and h and k are the coordinates of the vertex.  For us, p = .25, h = 7, and k = -6.  Filling in our formula:

4(.25)(y+6)=(x-7)^2

Simplify the left side to

1(y+6)=(x-7)^2 which simplifies, in its entirety, to

(x-7)^2-6=y

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Given :-

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<u>Taking</u><u> </u><u>second</u><u> </u><u>equation</u><u>:</u><u>-</u>

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<u>Substitute</u><u> </u><u>in </u><u>first </u><u>equation</u><u> </u><u>:</u><u>-</u><u> </u>

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<u>When </u><u>b </u><u>=</u><u> </u><u>0</u><u> </u><u>,</u>

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<u>When </u><u>a </u><u>=</u><u> </u><u>-</u><u>1</u><u> </u><u>,</u>

  • (-1)² - 2*(-1) - b² = 0
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<u>Answer </u><u>:</u><u>-</u><u> </u>

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