Answer:
To find the vertex of the parabola with the equation \( f(x) = 2x^2 + 12x + 14 \), you can use the formula:
\[ x = \frac{-b}{2a} \]
Where \( a = 2 \) and \( b = 12 \) from the equation \( f(x) = ax^2 + bx + c \).
Plugging in the values:
\[ x = \frac{-12}{2(2)} = \frac{-12}{4} = -3 \]
Now, to find the corresponding \( y \)-coordinate, plug \( x = -3 \) into the equation:
\[ f(-3) = 2(-3)^2 + 12(-3) + 14 \]
\[ f(-3) = 2(9) - 36 + 14 \]
\[ f(-3) = 18 - 36 + 14 \]
\[ f(-3) = -4 \]
So, the vertex of the parabola is \( (-3, -4) \).
