We are given the function <span>x^2+8x+4y+4=0. To determine the characteristics of this function, we need to write it in the standard form as follows:
</span><span>x^2+8x+4y+4=0
4y = -x^2 - 8x - 4
y = (-1/4)x^2 - 2x - 1
To determine the vertex and the focus of the parabola, we write it in the form </span>(y+k)^2 = x+h by completing the square method.
y + 1 = (-1/4)x^2 - 2x
y +1 = (-1/4)(x^2 + x/2)
y +1 - 1/64 = (-1/4)(x^2 + x/2 + 1/16)
y + 15/16 = (-1/4) (x + 1/4)^2
The vertex would be at point ( -1/4, -15/16)
The focus would be determined as follows:
<span>4p=-1/4 so p=-1/8
focus = (-1/4+(-1/8),-15/16) = (-3/8,-15/16)
Directrix = </span><span>x = h - p
x = -1/4 - -1/8 = -1/8 </span>
Answer:
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Step-by-step explanation:
