Question

Find the values of 2x2 by completing this chart.xx22x2−248−11200011224Fill in the blank text field 1

Answer 1

Step 1:

Draw and complete the chart

Step-by-step explanation

`\begin{gathered} \text{For x = -2, x}^2\text{ = \lparen-2\rparen}^2\text{ = 4 , 2x}^2\text{ = 2}*4\text{ = 8} \\ For\text{ x = -1 , x}^2\text{ = \lparen-1\rparen}^2\text{ = 1, 2x}^2\text{ = 2}*\text{ 1 = 1} \\ For\text{ x = 0, x}^2\text{ = 0}^2\text{ = 0 , 2x}^2\text{ = 2}*\text{ 0 = 0} \\ For\text{ x = 1, x}^2\text{ = 1}^2\text{ = 1, 2x}^2\text{ = 2 }*\text{ 1 = 2} \\ For\text{ x = 2 , x}^2\text{ = 2}^2\text{ = 4, 2x}^2\text{ = 2}*\text{ 4 = 8} \end{gathered}`
`\begin{gathered} \text{y = 3x}^2+\text{ 12x - 4} \\ To\text{ find the minimum value, find the first derivative} \\ (dy)/(dx)\text{ = 6x + 12} \\ 6x\text{ + 12 = 0} \\ 6x\text{ = -12} \\ x\text{ = }(-12)/(6)\text{ = -2} \end{gathered}`

Substitute x = -2, to find the minimum value.

`\begin{gathered} \text{y = 3x}^2+12x-4 \\ \text{y = 3}*(-2)^2\text{ + 12}*(-2)\text{ - 4} \\ \text{y = 12 - 24 - 4} \\ \text{y = -16} \end{gathered}`

The minimum value is (-2, -16)