Which Ratio is correct based on this diagram? a
The ratio of ears to paws to tails is 4:2:1
b
The ratio of ears to paws to tails is 2:4:1
c
The ratio of ears to paws to tails is 7:4:1
d
The ratio of ears to paws to tails is 7:2:1

Explanation:

The x intercepts always occur when y = 0. This is where the graph crosses the horizontal x axis.

Replace y with 0 and isolate x using the zero product property. This idea says that if A*B = 0, then either A = 0 or B = 0 or both are zero.

So,

y = -(x+1)(x-3)

-(x+1)(x-3) = y

-(x+1)(x-3) = 0

-(x+1) = 0 or x-3 = 0

x+1 = 0 or x-3 = 0

x = -1 or x = 3

The x intercepts are -1 and 3

The x coordinate of the vertex is exactly halfway between the two x intercepts. This is due to mirror symmetry about the vertex.

The midpoint of -1 and 3 is (-1+3)/2 = 2/2 = 1, which is plugged into the original equation to get

y = -(x+1)(x-3)

y = -(1+1)(1-3)

y = -(2)(-2)

y = 4

The vertex is the point (1, 4)