The vertex of this parabola is at (-3, 6). which of the following could be its equation?
A. y=-3(x-3)^2+6
B. y=-3(x+3)^2+6
C. y=-3(x-3)^2-6
D. y=-3(x+3)^2-6

Option B -  y=-3(x+3)^2+6

Step-by-step explanation:

Step 1:

The equation of any parabola in the standard form with vertex at the origin is y^2 = 4ax  . When it opens upward, the equation would be x^2 = 4ay

When the vertex is shifted to a point other than the origin, the equation would be

(x-h)^2 = 4a(y-k)

Step 2 :

Given that the vertex of the parabola is at  (-3, 6). We will have the x and y co-ordinate shifted with this value.

So the equation of the parabola will have x and y shifted to x-(-3)) and y-6

=> x+3 and y-6

Step 3:

Based on the above 2, we can see that option B  y=-3(x+3)^2+6 could be the equation of the parabola.

can you add an image ?

step-by-step explanation:

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