[tex]\displaystyle\bf\\y=3x^{2} +7x-6\\\\1)\\\\y(-5)=3\cdot(-5)^{2}+7\cdot(-5)-6=75-35-6=34\\\\y(10)=3\cdot 10^{2} +7\cdot 10-6=300+70-6=364\\\\y(1,5)=3\cdot 1,5^{2} +7\cdot 1,5-6=3\cdot 2,25+10,5-6=6,75+4,5=11,25\\\\\\2)\\\\y=-6\\\\-6=3x^{2} +7x-6\\\\3x^{2} +7x-6+6=0\\\\3x^{2} +7x=0\\\\x\cdot(3x+7)=0\\\\\boxed{x_{1}=0}\\\\3x+7=0\\\\\boxed{x_{2} =-2\frac{1}{3} }[/tex]

[tex]\displaystyle\bf\\y=0\\\\0=3x^{2} +7x-6\\\\3x^{2} +7x-6=0\\\\D=7^{2} -4\cdot 3\cdot (-6)=49+72=121=11^{2} \\\\\\x_{1} =\frac{-7-11}{6} =-3\\\\\\\boxed{x_{1} =-3}\\\\\\x_{2} =\frac{-7+11}{6} =\frac{2}{3} \\\\\\\boxed{x_{2} =\frac{2}{3}} \\\\\\3)\\\\X_{v} =-\frac{b}{2a} =-\frac{7}{2\cdot 3} =-\frac{7}{6} =-1\frac{1}{6} \\\\\\Y_{v} =3\cdot\bigg(-\frac{7}{6} \bigg)^{2} +7\cdot\bigg(-\frac{7}{6} \bigg)-6=-3\cdot \frac{49}{36} -\frac{49}{6} -6=[/tex]

[tex]\displaystyle\bf\\=-\frac{49}{12} -\frac{98}{12}-6=-\frac{147}{12} -6=-12,25-6=-18,25[/tex]

Координаты вершины параболы :

[tex]\displaystyle\bf\\\bigg(-1\frac{1}{6} \ ; \ -18,25\bigg)[/tex]

Прямая [tex]\displaystyle\bf\\X_{v} =-1\frac{1}{6} -[/tex]   ось симметрии параболы