Poopeyidn
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From the equation [tex][tex]$y = x^2 + 3x + 1$[/tex][/tex], find the axis of symmetry of the parabola.

A. [tex][tex]$x = \frac{3}{2}$[/tex][/tex]
B. [tex][tex]$x = 3$[/tex][/tex]
C. [tex][tex]$y = 1$[/tex][/tex]
D. [tex][tex]$x = -\frac{3}{2}$[/tex][/tex]

Please select the best answer from the choices provided:
A
B
C
D

Sagot :

GinnyAnsweridn
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]
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