Using a directrix of y = 5 with focus at (4, 1), what quadratic function is created? f(x) = 1/4(x − 4)2 − 3 f(x) = 1/8(x + 4)2 − 3 f(x) = −1/8(x − 4)2 + 3 f(x)
Mathematics
estauffer21
Question
Using a directrix of y = 5 with focus at (4, 1), what quadratic function is created?
f(x) = 1/4(x − 4)2 − 3
f(x) = 1/8(x + 4)2 − 3
f(x) = −1/8(x − 4)2 + 3
f(x) = 1/4(x + 4)2 − 3
f(x) = 1/4(x − 4)2 − 3
f(x) = 1/8(x + 4)2 − 3
f(x) = −1/8(x − 4)2 + 3
f(x) = 1/4(x + 4)2 − 3
1 Answer

1. User Answers jimrgrant1
Answer:
C
Stepbystep explanation:
From any point (x, y) on the parabola the focus and directrix are equidistant.
Using the distance formula
[tex]\sqrt{(x4)^2+(y1)^2}[/tex] =  y  5 
Squaring both sides
(x  4)² + (y  1)² = (y  5)² ← distribute the factors in y
(x  4)² + y²  2y + 1 = y²  10y + 25 ( subtract y²  10y + 25 from both sides )
(x  4)² + 8y  24 = 0 ( subtract (x  4)² from both sides )
8y  24 =  (x  4)² ← add 24 to both sides )
8y =  (x  4)² + 24 ( divide both sides by 8 )
y =  [tex]\frac{1}{8}[/tex] (x  4)² + 3
Hence
f(x) =  [tex]\frac{1}{8}[/tex] (x  4)² + 3 → C