To find the equation of the axis of symmetry of the parabola given by the equation [tex]\( y = x^2 + 4 \)[/tex], you can follow these steps:
1. Identify the general form of the quadratic equation: [tex]\( y = ax^2 + bx + c \)[/tex].
Here, the equation [tex]\( y = x^2 + 4 \)[/tex] can be written in the form [tex]\( y = ax^2 + bx + c \)[/tex].
2. Determine the coefficients [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex]:
- For [tex]\( y = x^2 + 4 \)[/tex]:
- [tex]\( a = 1 \)[/tex] (coefficient of [tex]\( x^2 \)[/tex])
- [tex]\( b = 0 \)[/tex] (coefficient of [tex]\( x \)[/tex])
- [tex]\( c = 4 \)[/tex] (constant term, although not needed for the axis of symmetry)
3. Use the formula for the axis of symmetry of a parabola, which is [tex]\( x = -\frac{b}{2a} \)[/tex].
4. Substitute the values of [tex]\( b \)[/tex] and [tex]\( a \)[/tex] into the formula:
- Here, [tex]\( b = 0 \)[/tex] and [tex]\( a = 1 \)[/tex].
So, the calculation is:
[tex]\[
x = -\frac{0}{2 \times 1} = 0
\][/tex]
5. Thus, the equation of the axis of symmetry is:
[tex]\[
x = 0
\][/tex]
Therefore, the equation of the axis of symmetry of the parabola [tex]\( y = x^2 + 4 \)[/tex] is [tex]\( x = 0 \)[/tex].
