Question

Analyze the given data:

The function that models the given data is.

• A. $y=2x^2$
• B. $y=3x^2$
• C. $y=5x^2$
• D. $y=4x^2$

Answer 1

The correct option is B $y=3x^2$


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.

$\text{Since, the second difference all are +6,}$
$\text{so, the function is a quadratic one}$
$i.e.y=a{x}^2$

Let us consider one point, say (2,12) from the table and substitute in the above equation.

$y=a{x}^2$

$\Rightarrow 12=a\left(2^2\right)$

$\Rightarrow 12=a\times 4$

$\Rightarrow \frac{12}{4}=a$

$\Rightarrow a=3$

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

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