Question

Evaluate the polynomial equation y equals 1/2 x 3 + 2 x 2 + 4x - 6 for each value of x

Answer 1

Given

`y=(1)/(2)x^3+2x^2+4x-6`

Assuming values of x in the range

`-2\leq x\leq2`

Substitute the values of x, which are {-2, -1 , 0, 1 , 2 }

`\begin{gathered} \text{For x= -2} \\ y=(1)/(2)(-2)^3+2(-2)^2+4(-2)-6_{} \end{gathered}`
`\begin{gathered} y=(1)/(2)(-8)+2(4)-8-6 \\ =-4+8-8-6 \\ =-10 \end{gathered}`
`\begin{gathered} \text{For x=-1} \\ y=(1)/(2)(-1)^3+2(-1)^2+4(-1)-6 \\ =(1)/(2)(-1)+2(1)-4-6 \\ =-(1)/(2)+2-4-6 \\ =-(17)/(2) \end{gathered}`
`\begin{gathered} \text{For x=0} \\ y=(1)/(2)(0)^3+2(0)^2+4(0)-6 \\ =-6 \end{gathered}`
`\begin{gathered} \text{For x=1} \\ y=(1)/(2)(1)^3+2(1)^2+4(1)-6 \\ =(1)/(2)(1)+2(1)+4-6 \\ =(1)/(2)+2+4-6 \\ =(1)/(2) \end{gathered}`
`\begin{gathered} \text{For x=1} \\ y=(1)/(2)(2)^3+2(2)^2+4(2)-6 \\ =(1)/(2)(8)+2(4)+8-6 \\ =4+8+8-6 \\ =14 \end{gathered}`

Present your workings in a table