What are the vertex, focus and directrix of y=x2+10x+21?

1 Answer
Mar 4, 2016

Vertex is 5,4), (focus is (5,154) and directrix is 4y+21=0

Explanation:

Vertex form of equation is y=a(xh)2+k where (h,k) is vertex

The given equation is y=x2+10x+21. It may be noted that the coefficient of y is 1 and that of x too is 1. Hence, for converting the same, we have to make terms containing x a complete square i.e.

y=x2+10x+2525+21 or

y=(x+5)24 or

y=(x(5))24

Hence vertex is (5,4)

Standard form of parabola is (xh)2=4p(yk),

where focus is (h,k+p) and directrix y=kp

As the given equation can be written as (x(5))2=4×14(y(4)), we have vertex (h,k) as (5,4) and

focus is (5,154) and directrix is y=514=214 or 4y+21=0