Question

Study the table.

x
y
–2
8
–1
2
0
0
1
2
2
8

Which best describes the function represented by the data in the table?
linear with a common ratio of 4
linear with a common second difference of 4
quadratic with a common ratio of 4
quadratic with a common second difference of 4

Answer 1

Answer:

quadratic with a common second difference of 4

Step-by-step explanation:

quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a$x^2$+ b$x$ + c = 0.

                               $\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right]$

from the table it is clear that,

function is y = 2$x^2$

so the function is not linear as the equation specifies.

formula to find second difference of a quadratic equation:

f(x + 2) - 2f(x + 1) + f(x)

therefore;

$2(x+2)^2$ - $4(x+1)^2$ + $2x^2$

$2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2$

$2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2$

$4x^2 - 4x^2 + 8x - 8x +8 - 4$

4

therefore, the answer is quadratic with a common second difference of 4

learn more about quadratic equations

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