# Given three points (-1,4) (1,6) (2,10) how do you write a quadratic function in standard form with the points?

##### 1 Answer

Solve a system of three equations in three unknowns.

#### Explanation:

Let us assume that the axis of symmetry for the parabola is vertical.

The standard equation of a parabola with a vertical axis is

Using the coordinates of the above points, we know that...

This simplifies to

We also have:

That is,

And finally:

The three equations give us the following system, which has a unique solution (a, b, c):

While we may solve these using any method, it will be convenient to subtract equation (1) from equation (2).

Change the signs and add:

Adding gives us:

Our system is now reduced to just two unknowns. Putting the known value of b into the three equations gives:

Simplify to:

Subtract the first from the second to obtain the equation:

Substitute a = 1 into the equation

The equation of our parabola has a = 1, b = 1, and c = 4.

Therefore, it is

Check, and you will find that all three points fit the equation.