# How do you find an equation in standard form of the parabola passing through the points (1,1), (-1, -3), (-3, 1)?

##### 1 Answer

Please see the explanation for steps leading to the answer:

#### Explanation:

There are two standard forms for a parabola:

Type 1 opens up or down:

Type 2 opens left or right:

Plot the 3 points:

The points look like they fit the first type.

Write 3 equations by substituting the 3 points into the type 1 form:

Move the coefficients in front of the variables:

Subtract equation [1] from equation [2]

Substitute 2 for b into equations [1] and [3]:

Subtract equation [1] from equation [3]:

Substitute 1 for a in equation [1]:

Confirm that the equation:

This checks.

The equation is