ANSWER
x = 2
EXPLANATION
We want to find the axis of symmetry of the equation:
[tex]y=-x^2\text{ + 4x + 3}[/tex]The axis of symmetry of a quadratic equation is given as:
[tex]\begin{gathered} \text{For:} \\ y=ax^2\text{ + bx + c} \\ \text{Axis of symmetry: } \\ x\text{ = -}\frac{b}{2a} \end{gathered}[/tex]From the given equation, a = -1 and b = 4
Therefore, the axis of symmetry is:
[tex]x\text{ = -}\frac{4}{2(-1)}\text{ = -}\frac{4}{-2}\text{ = }\frac{-4}{-2}[/tex]That is the axis of symmetry.