Verified answer

[tex]\displaystyle\bf\\f(x)=\frac{1}{2} x^{2} +3x\\\\\\1)\\\\f(1)=\frac{1}{2} \cdot 1^{2} +3\cdot 1=\frac{1}{2}+3=3,5 \\\\\\2)\\\\f(0)=\frac{1}{2} \cdot 0^{2} +3\cdot 0=0\\\\\\3)\\\\f(-4)=\frac{1}{2} \cdot (-4)^{2} +3\cdot (-4)=\frac{1}{2}\cdot 16-12=8-12=-4\\\\\\4)\\\\f\Big(-\frac{1}{3} \Big)=\frac{1}{2} \cdot \Big(-\frac{1}{3} \Big)^{2} +3\cdot \Big(-\frac{1}{3} \Big)=\frac{1}{2}\cdot\frac{1}{9}-1=\frac{1}{18} -1=-\frac{17}{18}[/tex]