# How do you find the equation of the quadratic function given (1,6), (3,26), (-2,21)?

##### 1 Answer

Please see the explanation for steps leading to the equation:

#### Explanation:

There are two standard equations for a parabola for the two different types of parabolas.

- The type that opens up or down:

- The type that opens left or right:

The points look like they belong to a parabola that opens up, therefore, we shall try to fit them the first equation:

Write 3 different equations using the 3 points:

Write these equations into an augmented matrix:

Multiply row 1 by -9 and add to row 2:

Multiply row 1 by -4 and add to row 3:

Subtract row 2 from row 3:

Divide row 3 by 5:

Multiply row 3 by 8 and add to row 2:

Divide row 2 by -6:

Subtract row 3 from row 1

Subtract row 2 from row 1:

Check:

This checks

The equation is: