What are the coordinates of the vertex of the graph of the function y = -3x^2 - 12x + 3?
To find the coordinates of the vertex of a quadratic function in the form y = ax^2 + bx + c, you can use the formula x = -b/2a to find the x-coordinate of the vertex, and then substitute this value back into the function to find the corresponding y-coordinate.
In this case, the function is y = -3x^2 - 12x + 3, so a = -3, b = -12, and c = 3.
First, find the x-coordinate of the vertex:
x = -b/2a
x = -(-12)/(2(-3))
x = 12/(-6)
x = -2
Now, substitute x = -2 back into the function to find the y-coordinate:
y = -3(-2)^2 - 12(-2) + 3
y = -3(4) + 24 + 3
y = -12 + 24 + 3
y = 15
Therefore, the coordinates of the vertex of the graph of the function y = -3x^2 - 12x + 3 are (-2, 15).
or, note that
-3x^2 - 12x + 3 = -3(x+2)^2 + 15
so the vertex is at (-2,15)