In the equation:
y = 3x² + 6x + 4
the leading coefficient, a, is equal to 3. Given that a is greater than zero, then the parabola has a shape of a U. Therefore, the parabola has a minimum.
To find the minimum, we need to find the vertex (h, k).
The x-coordinate of the vertex, h, is found as follows:
[tex]\begin{gathered} h=\frac{-b}{2a} \\ h=\frac{-6}{2\cdot3} \\ h=-1 \end{gathered}[/tex]The y-coordinate of the vertex, k, is found substituting h into the equation of the parabola, as follows:
[tex]\begin{gathered} y=3x^2+6x+4 \\ k=3h^2+6h+4 \\ k=3\cdot(-1)^2+6\cdot(-1)+4 \\ k=3\cdot1-6+4 \\ k=1 \end{gathered}[/tex]The minimum is placed at (-1, 1)
