What is the equation of the quadratic graph with a focus of (4, 3) and a directix of y = 13?

f(x) = −one twentieth (x − 4)2 + 10
f(x) = −one twentieth (x − 4)2 + 8
f(x) = one twentieth (x − 4)2 + 10
f(x) = one twentieth (x + 4)2 + 8

Recall that the equation of a parabola is given by 

where (h, k) is the vertex of the parabola and p is the distance between the vertex and the focus or directrix. The value of p is positive if the parabola is facing up and negative if the parabola is facing down.

The distance between the focus and the directrix is given by 13 - 3 = 10 and the distance from the vertex is half the distance from the directrix, therefore, the distance between the focus and the vertex is 5. Since the focus is below the directrix (i.e. the y value of the focus is 3 while the y value of the directrix is 13), the parabola describing the quadratic graph is facing down and the value of p is negative.

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.