Aparabola opens to the left. which could be the equation of the parabola?
a. (x – 4)2 = 4(y + 3)
b.(x – 4)2 = –4(y + 3)
c.(y – 4)2 = 4(x + 3)
d.(y – 4)2 = –4(x + 3)

option (d) is correct .

The parabola that opens to the left has equation

Step-by-step explanation:

Given : A parabola opens to the left.

We have to find that equation of parabola out of given options that opens to the left.

A parabola  that opens to left has parent equation of the form

On comparing with given options, if we apply translation shifting  y axis 4 units left and x axis 3 units upwards.

The graph is obtained as

Graph is attached below

Thus, option (d) is correct .

The parabola that opens to the left has equation

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

quit

step-by-step explanation: