What is the equation in the line of symmetry in the graph of y =2x² + 3x + 12

1 answer

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 \( x = -\frac{3}{4} \).