Write the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10).

Step-by-step explanation:

System Of Linear Equations

In this problem, we'll need to solve a 3x3 system of linear equations because we have three unknowns and three conditions.

We are required to find the equation of the quadratic function that passes through the points (-1, 1), (1, 5), and (2,10)

The general quadratic function can be written as

We need to find the values of a,b, and c. Let's use the first condition, i.e. f(-1)=1

Now we use the second condition f(1)=5

Finally, we use the third condition f(2)=10

We put together eq 1, eq 2, and eq 3 to form the system

Adding the first two equations we have

And also

Using the above equation and the value of b in the third equation, we have

Subtracting the first equation from the second

And therefore

Now we have all the values, the quadratic function is

go on the tube you might find some information there