Question

Study the table and find the value of output "y" at input "x" = 12.

• A. 86
• B. 84
• C. 106
• D. 96

Answer 1

The correct option is D 96


From the table, we observe:


As the first differences are not same, the function cannot be linear.

Here, the second differences are equal, the function is quardratic.

$\text{Since, the second difference all are}+\frac{4}{3},$
$\text{so, the function is a quadratic one}$
$i.e.y=a{x}^2$

$\text{Let us consider one point, say}(1,\frac{2}{3})$
from the table and substitute the value in the above equation.

$y=a{x}^2$

$\Rightarrow \frac{2}{3}=a\left(1^2\right)$

$\Rightarrow \frac{2}{3}=a$

$\Rightarrow a=\frac{2}{3}$

$\text{So,}y=\frac{2}{3}{x}^2$

$\text{∴ The equation of the data given}$
$\text{in table is}y=\frac{2}{3}{x}^2$

$\text{When x = 12, y}=\frac{2}{3}\times (12{)}^2=96$