To determine the axis of symmetry for the quadratic function [tex]\( h(x) = 5x^2 + 40x + 64 \)[/tex], we use the formula for the axis of symmetry of a quadratic equation of the form [tex]\( ax^2 + bx + c \)[/tex]. The formula is:
[tex]\[ x = \frac{-b}{2a} \][/tex]
In this quadratic function, the coefficients are:
- [tex]\( a = 5 \)[/tex]
- [tex]\( b = 40 \)[/tex]
Plugging these values into the formula, we get:
[tex]\[ x = \frac{-40}{2 \cdot 5} \][/tex]
[tex]\[ x = \frac{-40}{10} \][/tex]
[tex]\[ x = -4 \][/tex]
Therefore, the axis of symmetry for the quadratic function [tex]\( h(x) = 5x^2 + 40x + 64 \)[/tex] is:
[tex]\[ x = -4 \][/tex]
So, the correct answer is:
[tex]\[ x = -4 \][/tex]
