Select all the numbers that logan could multiply by 54,216 to get a product less than 54,216

Explanation:

Recall that vertex form is

y = a(x-h)^2 + k

where (h,k) is the vertex. We want the vertex to be (-3,0) which means that h = -3 and k = 0 must be the case.

Plug those values in to get

y = a(x-h)^2 + k

y = a(x-(-3))^2 + 0

y = a(x+3)^2

Now we need the value of 'a', which determines two things

To determine 'a', we'll use the other point (-5,-4).

So we'll plug in x = -5 and y = -4 and solve for 'a'

y = a(x+3)^2

-4 = a(-5+3)^2

-4 = a(-2)^2

-4 = a(4)

-4 = 4a

4a = -4

a = -4/4

a = -1

The equation y = a(x+3)^2 updates to y = -1(x+3)^2 which simplifies to the final answer y = -(x+3)^2. The answer is choice D.

As a check, plugging x = -5 should lead to y = -4

y = -(x+3)^2

y = -(-5+3)^2

y = -(-2)^2

y = -(4)

y = -4

This helps confirm the answer.

I'll let you check to see if (-3,0) is on this graph. Plugging in x = -3 should lead to y = 0.