For Exercise, an equation of a parabola is given in standard form.a. Determine the value of pb. Identify the vertex.c. Identify the focus.d. Determine the focal diameter.e. Determine the endpoints of the latus rectum.f. Write an equation of the directrix.g. Write an equation for the axis of symmetry.h. Graph the parabola. (y + 2)2 = −4(x − 3).

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Asked Dec 24, 2019
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For Exercise, an equation of a parabola is given in standard form.

a. Determine the value of p

b. Identify the vertex.

c. Identify the focus.

d. Determine the focal diameter.

e. Determine the endpoints of the latus rectum.

f. Write an equation of the directrix.

g. Write an equation for the axis of symmetry.

h. Graph the parabola. (y + 2)2 = −4(x − 3).

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Expert Answer

Step 1

Given equation of parabola in standard form:

 

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(у+2) 3- 4(х - 3)

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Step 2

a.  Determine of the value of p.

Here is the standard form of parabola, where

(h,k) is vertex .

Now compare the given parabola equation with standard equation of parabola.

So, value of p = -1

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(у+2)? %3- 4(х - 3) (у-к) — 4p(x- - h) 4 p =-4 p=-1

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Step 3

b.  Identify the vertex.

Here (h,k) is vertex ...

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(y+2) = -4(x–3) (y-k)' = 4p(x- h) h= 3 k = -2 Vertex = (3,–2)

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