To find the equation of the axis of symmetry for the given parabola represented by the equation \( y = -2x^2 + 8x + 6 \), we can use the formula for the axis of symmetry for a quadratic function of the form \( y = ax^2 + bx + c \). The formula for the axis of symmetry is given by:
\[ x = -\frac{b}{2a} \]
In the given equation, we identify the coefficients:
- \( a = -2 \)
- \( b = 8 \)
- \( c = 6 \) (we won't use this for the axis of symmetry calculation).
Now, we substitute the values of \( a \) and \( b \) into the formula:
\[ x = -\frac{8}{2 \cdot -2} \]
Calculating the denominator:
\[ 2 \cdot -2 = -4 \]
Now, substituting this back into the equation gives:
\[ x = -\frac{8}{-4} \] \[ x = 2 \]
Thus, the equation of the axis of symmetry for the parabola is:
\[ x = 2 \]
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