Question

The variables x and y have a quadratic relationship. Tripling the value of x causes the value of y to increase by a factor of nine. When x has a value of 3, y has a value of 2. What will be the value of y when x has a value of 9?​

Answer 1

The value of y when x has a value of 9 is 18

Explanation:

Functions

The variables x and y are said to have a quadratic relationship. That information is not enough to set up a general equation for both variables.

Furthermore, we know that tripling the value of x causes the value of y to be multiplied by 9. That leads us to establish a proportional equation between them, as follows:

`y=kx^2`

Where k is an unknown constant.

Let's use the given point (3,2) to find the value of k:

`2=k(3)^2`

`2=9k`

Solving for k:

`\displaystyle k=(2)/(9)`

The equation is now:

`\displaystyle y=(2)/(9)x^2`

Now find y when x=9:

`\displaystyle y=(2)/(9)(9)^2`

`\displaystyle y=(2)/(9)\cdot 81=18`

The value of y when x has a value of 9 is 18