Question

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

Answer 1

Given

$y=\frac{1}{2}x^3+2x^2+4x-6$

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

Present your workings in a table