To find the equation of the axis of symmetry of the parabola given by the equation \( y = 2x^2 - 16x + 42 \), we can use the formula for the axis of symmetry for a parabola in the form \( y = ax^2 + bx + c \). The axis of symmetry can be found using the formula:
\[ x = -\frac{b}{2a} \]
where \( a \) and \( b \) are the coefficients from the quadratic equation \( ax^2 + bx + c \).
In this case, we have:
- \( a = 2 \)
- \( b = -16 \)
- \( c = 42 \) (though we don't need \( c \) for this calculation)
Now we can substitute \( a \) and \( b \) into the formula:
\[ x = -\frac{-16}{2 \cdot 2} = \frac{16}{4} = 4 \]
Thus, the equation of the axis of symmetry is \( x = 4 \).
1 answer