To find the x value of the vertex we do:
x = [tex] \frac{-b}{2a} [/tex]
if your quadratic function is in the form ax² + bx + c = y
x = [tex] \frac{-3}{2(1)} [/tex]
x = [tex] \frac{-3}{2} [/tex]
Now we plug this x into the equation and solve for y.
y = [tex] (\frac{-3}{2}) ^{2} + 3( \frac{-3}{2} ) + 4[/tex]
y = [tex] \frac{9}{4} - \frac{9}{2} + 4 [/tex]
y = [tex] \frac{9}{4} - \frac{18}{4} + 4[/tex]
y = [tex] \frac{-9}{4} + 4[/tex]
y = [tex] \frac{-9}{4} + \frac{16}{4} [/tex]
y = [tex] \frac{7}{4} [/tex]
Your vertex (if my math is correct) is at [tex]( \frac{-3}{2}, \frac{7}{4} )[/tex]
