Question

Determine if the following table represents a quadratic function. X 1 2 3 4 5 Y 13 22 37 58 85

Answer 1

Yes, the table represents quadratic function.

`Y = 3X^2+10`

Explanation:

Given that table of values:

`\begin{center}\begin{tabular}{ c c}X & Y \\ 1 & 13 \\ 2 & 22 \\ 3 & 37 \\ 4 & 58 \\ 5 & 85 \\\end{tabular}\end{center}`

To find:

Whether the given table represents a quadratic?

Solution:

First of all, let us plot the given values on the coordinate xy plane.

Kindly refer to the attached image for the graph of given values.

The graph seems parabolic in nature which is the graph of a quadratic equation.

Now, let us try to find the equation from the given set of values from hit and trial.

Let Quadratic equation be:

`y=ax^(2) +b`

If the coefficient a = 1

`f(1) = 13 = 1^2+12`

`f(2) = 22 = 2^2+18`

`f(3) = 37= 3^2+28`

`f(4) = 58 = 4^2+42`

`f(5) = 85 = 5^2+60`

value of b is not same in each case.

Now, let us try coefficient a = 3

`f(1) = 13 = 3 * 1^2+10`

`f(2) = 22 = 3* 2^2+10`

`f(3) = 37= 3* 3^2+10`

`f(4) = 58 = 3* 4^2+10`

`f(5) = 85 =3* 5^2+10`

Value of b = 10

So, we can clearly say that the given table represents a quadratic equation.

and the quadratic equation is:

`Y = 3X^2+10`