Write an equation for the parabola.
-vertex (4, 8), focus (4, 10)
A) $y - 8 = 8 ( x - 4 ) ^ { 2 }$
B) $8 ( y - 8 ) = ( x - 4 ) ^ { 2 }$
C) $2 ( y - 8 ) = ( x - 4 ) ^ { 2 }$
D) $( y - 8 ) ^ { 2 } = 8 ( x - 4 )$

Question

Write an equation for the parabola.
-vertex (4, 8), focus (4, 10) 
A) $y - 8 = 8 ( x - 4 ) ^ { 2 }$
B) $8 ( y - 8 ) = ( x - 4 ) ^ { 2 }$
C) $2 ( y - 8 ) = ( x - 4 ) ^ { 2 }$
D) $( y - 8 ) ^ { 2 } = 8 ( x - 4 )$

Quizplus · Accepted Answer

The focus is 2 units above the vertex, indicating a vertical parabola opening upwards. The distance from the vertex to the focus (p) is 2, so the equation is $4p(y - k) = (x - h)^2$, where (h, k) is the vertex. Substituting $h = 4$, $k = 8$, and $p = 2$ gives $8(y - 8) = (x - 4)^2$.

Write an Equation for the Parabola y−8=8(x−4)2y - 8 = 8 ( x - 4 ) ^ { 2 }y−8=8(x−4)2

Write an Equation for the Parabola $y - 8 = 8 ( x - 4 ) ^ { 2 }$