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altavistard
This parab. is a vertical one, opening down.  
The standard equation of a parabola appying here is 4p(y-k) = (x-h)^2.
Take the values of h and k from the given vertex and subst. them into this equation:

4p(y-1) = (x+3)^2

Now p is the distance between vertex and directrix; that distance is 5 units (which is 6 less 1).  Thus, the equation of the parabola becomes

4(5)(y-1) = (x+3)^2, or y-1 = (1/20)(x+3)^2    (answer)

If the vertex of a parabola is (-3, 1) and its directrix y = 6. Then the equation of the parabola will be given below.

[tex]\rm y-1 = \dfrac{1}{20}(x+3)^2[/tex]

What is the parabola?

It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.

The vertex of a parabola is (-3, 1) and its directrix y = 6.

Then the equation will be

[tex]\rm 4p(y-1) = (x+3)^2[/tex]

The distance between the vertex and the directrix is now p; it is 5 units (which is 6 less 1). As a result, the parabola equation becomes

[tex]\begin{aligned} \rm 4(5)(y-1) &= \rm (x+3)^2\\\\\rm y-1 &= \rm \dfrac{1}{20}(x+3)^2 \end{aligned}[/tex]

More about the parabola link is given below.

https://brainly.com/question/8495504

#SPJ2

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