To find the equation of the axis of symmetry for the given quadratic function [tex]\( y = 5x^2 + 20x + 1 \)[/tex], we can follow these steps:
1. Identify the coefficients: Look at the standard form of a quadratic equation, which is [tex]\( y = ax^2 + bx + c \)[/tex]. Here, the coefficients are:
- [tex]\( a = 5 \)[/tex]
- [tex]\( b = 20 \)[/tex]
- [tex]\( c = 1 \)[/tex] (although [tex]\( c \)[/tex] is not needed to find the axis of symmetry)
2. Use the formula for the axis of symmetry: The formula to find the axis of symmetry for a quadratic equation [tex]\( y = ax^2 + bx + c \)[/tex] is:
[tex]\[
x = -\frac{b}{2a}
\][/tex]
3. Substitute the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex] into the formula:
[tex]\[
x = -\frac{20}{2(5)}
\][/tex]
4. Simplify the expression:
[tex]\[
x = -\frac{20}{10}
= -2
\][/tex]
Hence, the equation of the axis of symmetry for the quadratic function [tex]\( y = 5x^2 + 20x + 1 \)[/tex] is [tex]\( x = -2 \)[/tex].
Therefore, the correct answer is:
[tex]\[
x = -2
\][/tex]
