Question

Select the correct answer. Which equation describes the function modeled in this table? 1 -2. -1 0 1 2 3 4 6 0 0 (more 6 16 30 OA. Y O B. Y (2x - 1)(x - 1) 2(x - 1)? 2(x + 1)2 2x2 – 2 O C. y = D. y

Answer 1

Given:-

A set of data.

To find the required equation.

So from the given equation, the equation which suits is,

$y=2x^2-2$

So now we prove it by substituting the values from the table.

When x=-2 we get the value as,

$\begin{gathered} y=2x^2-2 \\ y=2(-2)^2-2 \\ y=2\times4-2 \\ y=8-2 \\ y=6 \end{gathered}$

So the value of y is 6.

When x=-1. we get,

$\begin{gathered} y=2x^2-2 \\ y=2(-1)^2-2 \\ y=2\times1-2 \\ y=2-2 \\ y=0 \end{gathered}$

So the value of y is 0.

When x=0. we get,

$\begin{gathered} y=2x^2-2 \\ y=2(0)-2 \\ y=-2 \end{gathered}$

So the value of y is -2.

When x=1. we get,

$\begin{gathered} y=2x^2-2 \\ y=2(1)-2 \\ y=2-2 \\ y=0 \end{gathered}$

So the value of y is 0.

When x=2. we get,

$\begin{gathered} y=2x^2-2 \\ y=2(2)^2-2 \\ y=2\times4-2 \\ y=8-2 \\ y=6 \end{gathered}$

So the value of y is 6.

When x=3. we get,

$\begin{gathered} y=2x^2-2 \\ y=2(3)^2-2 \\ y=2\times9-2 \\ y=18-2 \\ y=16 \end{gathered}$

So the value of y is 16.

When x=4. we get,

$\begin{gathered} y=2x^2-2 \\ y=2(4)^2-2 \\ y=2\times16-2 \\ y=32-2 \\ y=30 \end{gathered}$

So the value of y is 30.

So from this we can conclude that the correct equation is,

$y=2x^2-2$