To determine the axis of symmetry for the quadratic equation [tex]\( f(x) = 10x^2 - 20x + 16 \)[/tex], we use the formula for the axis of symmetry of a parabola, which is given by:
[tex]\[
x = \frac{-b}{2a}
\][/tex]
Here, the equation is written in the standard form [tex]\( ax^2 + bx + c \)[/tex], where:
- [tex]\( a = 10 \)[/tex]
- [tex]\( b = -20 \)[/tex]
Substituting these values into the formula for the axis of symmetry, we get:
[tex]\[
x = \frac{-(-20)}{2 \cdot 10} = \frac{20}{20} = 1
\][/tex]
Therefore, the axis of symmetry of the parabola described by the equation [tex]\( f(x) = 10x^2 - 20x + 16 \)[/tex] is [tex]\( x = 1 \)[/tex].
Among the choices provided, the correct answer is:
c. [tex]\( x = 1 \)[/tex]
So, the best answer from the choices provided is:
C [tex]\( x=1 \)[/tex]
