Find the equation of the axis of symmetry of the following parabola algebraically.

y, equals, 2, x, squared, minus, 16, x, plus, 42
y=2x
2
−16x+42

1 answer

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 \( x = 4 \).