We are given . This can be rewritten as .
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
The values of x are
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function.
The first equation is .
The second equation is .
Factoring, we have
Equating both factors to zero.
When the value of x is 6, the value of y is
When the value of x is -3, the value of y is
Therefore, the solutions are (6,38) or (-3,11)
The first differences would be as follows:
11.5 - 7 = 4.5
7 - 3.5 = 3.5
3.5 - 1 = 2.5
1 - -0.5 = 1.5
-0.5 - - 1 = 0.5
Since they are not the same, it is not linear.
The second differences would be:
4.5 - 3.5 = 1
3.5 - 2.5 = 1
2.5 - 1.5 = 1
1.5 - 0.5 = 1
Since the second differences are the same, it is a quadratic relationship.
If you look at the values on the left, the x-values, you can see that they are neatly lined up for us and they are increasing by 1.
Now, look at the y-values, they are increasing by adding 1/2.
When you have a constant increase of a value by addition or subtraction, it will create a linear pattern. You can also graph the equation to see the linear pattern.
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1/5^2 = 7.56/45