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Amit · Accepted Answer

5. 
                          (?)? = ?2 − 4
For finding the value of a, b, c  
Take the equation, ??2 + ?? + ? = 0                                                (1) 
By using equation 1 we can find the value of a, b, c
Coefficient of, ?2 = 1 = ? 
Coefficient of, ? = 0 = ? 
c=-4 
So, we have a=1, b=0, c=-4
Parabola equation for vertex 
?(? + ?)2 + ?                                                                                             (2) 
? =
?
2?
=0 
? = ? −
?2
4?
 
? = −4 
Substitute the value of a, d, e in (2) 
(? + 0)2 − 4
? = (? + 0)2 − 4                                                                                      (3)
Now, by using vertex form 
? = ?(? − ℎ)2 + ?                                                                                        (4) 
By comparing equation (3) and (4) 
 ? = −4 , h=0, a=1 
Vertex (h,k)=(0,-4) 
distance from the vertex to a focus of the parabola, p= 
1
4?
= 0.25  
focus= (h, p+k) = (0,0.25+(-4)) = (0,−
15
4
) 
axis of symmetry, x=0 
directrix of parabola, y = (k-p) = -4-0.25= (−
17
4
) 
Now,

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