To find the axis of symmetry of a parabola given by the quadratic equation [tex]\( y = x^2 + 3x + 1 \)[/tex], we can use the standard formula for the axis of symmetry. The general form of a quadratic equation is:
[tex]\[ y = ax^2 + bx + c \][/tex]
For the given equation [tex]\( y = x^2 + 3x + 1 \)[/tex], we can identify the coefficients as follows:
- [tex]\( a = 1 \)[/tex]
- [tex]\( b = 3 \)[/tex]
- [tex]\( c = 1 \)[/tex]
The formula for the axis of symmetry of a parabola is given by:
[tex]\[ x = -\frac{b}{2a} \][/tex]
Substituting the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula, we get:
[tex]\[ x = -\frac{3}{2 \cdot 1} \][/tex]
[tex]\[ x = -\frac{3}{2} \][/tex]
[tex]\[ x = -1.5 \][/tex]
Thus, the axis of symmetry for the given parabola is [tex]\( x = -\frac{3}{2} \)[/tex].
Therefore, the correct answer is:
D. [tex]\( x = -\frac{3}{2} \)[/tex]
