Question

Determine the equation of the graph and select the correct answer below.

Courtesy of Texas Instruments (6 points)

Answer 1

f(x+2)= -x^2 -4. Use basic transformations

Answer 2

The standard equation of parabola:

`y =a(x-h)^2+k` ....[1]

where, vertex = (h, k) and a is any constant value.

As per the statement:

In the given graph of parabola:

Vertex of parabola = (-2, -4)

⇒h = -2 and k= -4

Substitute in [1] we have;

`y =a(x+2)^2-4` ....[2]

Since, the graph of parabola cuts at y-axis at (0, -8)

Substitute this point in [2] to solve for a, we have;'

`-8=a(0+2)^2-4`

⇒
`-8=a(2)^2-4`

Add 4 to both sides we have;

`-4=a(2)^2`

⇒
`-4=4a`

Divide both sides by 4 we have;

a = -1

then, the equation become:

`y =-1(x+2)^2-4`

Therefore, the equation of the graph is,
`y =-(x+2)^2-4`