To find the equation of the line of symmetry for the quadratic function given by \( y = 2x^2 + 3x + 12 \), we can use the formula for the line of symmetry of a parabola, which is given by:
\[ x = -\frac{b}{2a} \]
where \( a \) and \( b \) are the coefficients from the quadratic equation \( ax^2 + bx + c \).
In this case, the coefficients are:
- \( a = 2 \)
- \( b = 3 \)
- \( c = 12 \) (though \( c \) is not needed to find the line of symmetry).
Now, substituting the values of \( a \) and \( b \) into the formula:
\[ x = -\frac{3}{2 \times 2} = -\frac{3}{4} \]
Thus, the equation of the line of symmetry is:
\[ x = -\frac{3}{4} \]
This line of symmetry means that the graph of the quadratic function is symmetric about the vertical line \( x = -\frac{3}{4} \).