Answer:
the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).
Explanation:
To rewrite the quadratic equation y=3x^2 + 12x + 14 into vertex form, we need to complete the square.
First, we can factor out the coefficient of x^2, which is 3:
y = 3(x^2 + 4x) + 14
Next, we need to add and subtract a constant term inside the parentheses that will allow us to complete the square. We can do this by adding and subtracting (4/2)^2 = 4:
y = 3(x^2 + 4x + 4 - 4) + 14
Now we can write the first three terms inside the parentheses as a squared expression:
y = 3((x + 2)^2 - 4) + 14
Finally, we can simplify this equation by distributing the 3 and combining like terms:
y = 3(x + 2)^2 - 2
So the vertex form of the quadratic equation y=3x^2 + 12x + 14 is y = 3(x + 2)^2 - 2. The vertex of this parabola is located at the point (-2, -2).