Question

Select the table of values that you would use to graph f(x) = 3x2 - 4.

Answer 1

The value which staisfy the equation are the coordinate of the f(x)

`f(x)=3x^2-4`

A) Table :

`\begin{gathered} at\text{ (-2,-8)} \\ f(-2)=3(-2)^2-4 \\ f(-2)=12-4 \\ f(-2)=8 \\ \text{but we have y =-8} \\ -8\\e8,\text{ } \end{gathered}`

So, the given table is not the solution of f(x)

B) Table :

`\begin{gathered} at\text{ (-2,9)} \\ f(-2)=3(-2)^2-4 \\ f(-2)=12-4 \\ f(-2)=8 \\ \text{but we have y =}9 \\ -8\\e9,\text{ } \end{gathered}`

the given table is not the solution of f(x)

C) table:

`\begin{gathered} at\text{ (-2,9)} \\ f(-2)=3(-2)^2-4 \\ f(-2)=12-4 \\ f(-2)=8 \\ and\text{ we have y =}8 \\ 8=8,\text{ } \end{gathered}`

now, for next coordinate :

`\begin{gathered} at\text{ (-1,-1)} \\ f(-1)=3(-1)^2-4 \\ f(-1)=3-4 \\ f(-1)=-1 \\ and\text{ we have y =}-1 \\ -1=-1,\text{ } \end{gathered}`
`\begin{gathered} at\text{ (0,-4)} \\ f(0)=3(0)^2-4 \\ f(0)=0-4 \\ f(0)=-4 \\ and\text{ we have y =}-4 \\ -4=-4,\text{ } \end{gathered}`
`\begin{gathered} at\text{ (1,-1)} \\ f(-1)=3(1)^2-4 \\ f(-1)=3-4 \\ f(-1)=-1 \\ and\text{ we have y =}-1 \\ -1=-1,\text{ } \end{gathered}`
`\begin{gathered} at\text{ (2,}8\text{)} \\ f(2)=3(2)^2-4 \\ f(2)=12-4 \\ f(2)=8 \\ and\text{ we have y =}8 \\ 8=8\text{ } \end{gathered}`

Since all the value staisfy the equation

Thus, The table is solution of the f(x)

D) table :

`\begin{gathered} at\text{ (-2,6)} \\ f(-2)=3(-2)^2-4 \\ f(-2)=12-4 \\ f(-2)=8 \\ but\text{we have y =}6 \\ 6\\e8\text{ } \end{gathered}`

Thus, the given table is not the solution of f(x)

Answer : C)