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:
[tex]y=kx^2[/tex]
Where k is an unknown constant.
Let's use the given point (3,2) to find the value of k:
[tex]2=k(3)^2[/tex]
[tex]2=9k[/tex]
Solving for k:
[tex]\displaystyle k=\frac{2}{9}[/tex]
The equation is now:
[tex]\displaystyle y=\frac{2}{9}x^2[/tex]
Now find y when x=9:
[tex]\displaystyle y=\frac{2}{9}(9)^2[/tex]
[tex]\displaystyle y=\frac{2}{9}\cdot 81=18[/tex]
The value of y when x has a value of 9 is 18
