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

Answer:

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

Step-by-step 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:

$\displaystyle k=\frac{2}{9}$

The equation is now:

$\displaystyle y=\frac{2}{9}x^2$

Now find y when x=9:

$\displaystyle y=\frac{2}{9}(9)^2$

$\displaystyle y=\frac{2}{9}\cdot 81=18$

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