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Answer:
Part 1) The vertex is the point (-83,-9)
Part 2) The focus is the point (-82.75,-9)
Part 3) The directrix is
Step-by-step explanation:
step 1
Find the vertex
we know that
The equation of a horizontal parabola in the standard form is equal to
where
p≠ 0.
(h,k) is the vertex
(h + p, k) is the focus
x=h-p is the directrix
In this problem we have
Convert to standard form
so
This is a horizontal parabola open to the right
(h,k) is the point (-83,-9)
so
The vertex is the point (-83,-9)
step 2
we have
<em>Find the value of p</em>
<em>Find the focus</em>
(h + p, k) is the focus
substitute
(-83+1/4,-9)
The focus is the point (-82.75,-9)
step 3
Find the directrix
The directrix of a horizontal parabola is
substitute