What are the coordinates of the vertex of the graph of the function y = –3x² –12x + 3?
To find the coordinates of the vertex of the graph of the function y = –3x² –12x + 3, we need to first determine the x-coordinate of the vertex.
The x-coordinate of the vertex of a parabola given by the equation y = ax² + bx + c is given by x = -b/(2a). In this case, the coefficient of x² is -3 and the coefficient of x is -12, so we have a = -3 and b = -12. Plugging these values into the formula x = -b/(2a), we get x = -(-12)/(2*(-3)) = 12/(-6) = -2.
Now that we have the x-coordinate of the vertex, we can find the y-coordinate by plugging this value into the original equation.
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 = –3x² –12x + 3 are (-2, 15).