+491
What is the equation of the directrix of this parabola?
y = -5/8x^2 -3x + 4
+128475 y = (-5/8)x^2 - 3x + 4
y - 4 = (-5/8)x^2 - 3x complete the square on the right
y - 4 = (-5/8) [ x^2 + 24/5x + 576/100 - 576/100]
y - 4 = (-5/8) [ x + 24/10]^2 + 18/5
y - 4 - 18/5 = (-5/8)[x + 24/10]^2
(y - 38/5) = (-5/8)[ x + 24/10]^2 multiply both sides by -8/5
(-8/5) (y - 38/5) = ( x + 24/10)^2
The vertex is ( -24/10, 38/5) = ( -12/5, 38/5)
Using the form
4p (y - k) = (x - h)^2
4p = -8/5
p = -2/5
This parabola turns downward so the equation of the directrix is
y =
38/5 - p
38/5 - (-2/5) =
8
So y = 8
