Resolvendo:
a) Correta.
[tex]f(x)=2x^{2} +5x+3\\2x^{2} +5x+3=0\\\\delta=b^{2} -4ac\\delta=5^{2} -4\:.\:2\:.\:3\\delta=25-24\\delta=1\\\\x'=\frac{-b+\sqrt{delta} }{2a} \\\\x'=\frac{-5+\sqrt{1} }{2\:.\:2} \\\\x'=\frac{-5+1}{4} \\\\x'=\frac{-4}{4} \\\\x'=-1\\\\\\x''=\frac{-b-\sqrt{delta} }{2a} \\\\x''=\frac{-5-1}{2\:.\:2} \\\\x''=\frac{-6}{4} \\\\x''=-\frac{3}{2}[/tex]
b) Correta.
a > 0 → Concavidade para cima
c) Correta.
[tex]x_{v} =\frac{-b}{2a} \\\\x_{v} =\frac{-5}{2\:.\:2} \\\\x_{v} =-\frac{5}{4} \\\\\\y_{v} =\frac{-delta}{4a} \\\\y_{v} =\frac{-1}{4\:.\:2} \\\\y_{v} =-\frac{1}{8}[/tex]
d) Incorreta.
[tex]f(x)=2x^{2} +5x+3\\y=2\:.\:0^{2} +5\:.\:0+3\\y=0+0+3\\y=3[/tex]
A intersecção com o eixo 0y seria ( 0; 3 ).
Assim, letra D.
Espero ter ajudado!
Desculpe qualquer erro.
