Verified answer

[tex]y = - {x}^{2} + 3x + 1[/tex]

[tex]a = - 1[/tex]

[tex]b = 3[/tex]

[tex]x = - \frac{3}{2 \times ( - 1)} [/tex]

[tex]x = \frac{3}{2} [/tex]

[tex]y = - {x}^{2} + 3x + 1[/tex]

[tex]x = \frac{3}{2} [/tex]

[tex]y = \frac{13}{4} [/tex]

[tex]( \frac{3}{2}, \frac{13}{4}) [/tex]