What are the coordinates of the vertex of the graph of the function y = -3x^2 -12x - 3?
To find the vertex of the graph 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, and then plug that value back into the original equation to find the y-coordinate.
In this case, the function is y = -3x^2 -12x - 3, and the coefficients are a = -3, b = -12, and c = -3.
To find the x-coordinate of the vertex, use the formula x = -b/(2a):
x = -(-12)/(2*(-3))
x = 12/(-6)
x = -2
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by plugging x = -2 back into the original equation:
y = -3*(-2)^2 - 12*(-2) - 3
y = -3*4 + 24 - 3
y = -12 + 24 - 3
y = 9
Therefore, the vertex of the graph of the function y = -3x^2 -12x - 3 is at (-2, 9).