Final answer:
To find the vertex of the quadratic function y=3x²+12x+4, we use the vertex formula, resulting in the vertex coordinates (-2, -8).
Step-by-step explanation:
The question asks for the coordinates of the vertex of the quadratic function y=3x²+12x+4. To find the vertex of a parabola, we can use the vertex formula, which is given by (-b/2a, f(-b/2a)), where 'a' and 'b' are coefficients from the quadratic equation y=ax²+bx+c. In this case, 'a' is 3 and 'b' is 12.
First, calculate the x-coordinate of the vertex:
- x = -b/(2a) = -12/(2×3) = -12/6 = -2
Next, substitute the x-coordinate back into the equation to find the y-coordinate:
- y = 3(-2)² + 12(-2) + 4 = 3(4) - 24 + 4 = 12 - 24 + 4 = -8
Hence, the vertex of the parabola is at the coordinates (-2, -8).