Question

The vertex of this parabola Is at (-3,6) which of the following could be its equation

Answer 1

Explanation:

the e standard form of parabola with vertex (h,k) is

y=a(x-h)²+k

here (h,k)=(-3,6)

so the answer to your question is

y=-3(x-(-3))²+6

y=-3(x+3)²+6

Answer 2

Option D is correct.

Explanation:

The vertex is (-3,6)

We will check which equation satisfies the given vertex.

A) y = -3(x-3)^2 - 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3-3)^2 - 6

y = -3(-6)^2 - 6

y = -3(36) -6

y = -114

if x= -3, y ≠ 6

B) y = -3(x+3)^2 - 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3+3)^2 - 6

y = -3(0)-6

y = -6

if x= -3, y ≠ 6

C) y = -3(x-3)^2 + 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3-3)^2 + 6

y = -3(-6)^2 + 6

y = -3(36) + 6

y = -102

if x= -3, y ≠ 6

D) y = -3(x+3)^2 + 6

if x = -3 then value of y should be 6

Checking:

y = -3(-3+3)^2 + 6

y = -3(0)^2 + 6

y = 6

So, if x= -3, y =6 so, if the vertex of parabola is at (-3,6) the equation will be

y = -3(x+3)^2 + 6

So. Option D is correct.