The equation of a parabola is given. y=−16x2+7x−80 What is the equation of the directrix of the parabola? Enter your answer in the box.

1 Answer
Douglas K.
May 24, 2018

y=−5

Explanation:

When given the equation of a parabola in the form,

y=ax2+bx+c

, the x coordinate of the vertex, h, can be found using the formula:

h=−b2a

The y coordinate of the vertex, k, is found by evaluating the function at h:

k=a(h)2+b(h)+c

The focal distance, f, can be found, using the formula:

f=14(a)

The equation of the directrix can be found, using the form:

y=k−f

Given: y=−16x2+7x−80

Please observe that a=−16andb=7, therefore, the x coordinate of the vertex is:

h=−72(−16)=422

h=21

The y coordinate, k, of the vertex can be found by evaluating the function at 21:

k=−16(21)2+7(21)−80

k=−132

The focal distance f is:

f=14(−16)=−64

f=−32

The equation of the directrix is:

y=−132−−32=−13+32=−102

y=−5

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