# What is the quadratic function of a graph if the points are (-2, -4) (-1, -2.5) (0, 0) (1, 3.5) (2, 8)?

##### 1 Answer

It can be guessed since we deal with easy numbers, but let's approach this problem theoretically.

The general equation of a quadratic function looks like this:

There are three unknown coefficients here -

Let's use three points out of 5 given to determine these three coefficients.

Point

or, simplifying this,

(1)

Point

or, simplifying this,

(2)

Point

or, simplifying this,

(3)

Equations (1), (2) and (3) constitute a system of 3 linear equations with three unknown variables. Let's solve it by substitution.

Step 1.

Substitute

(1)

(2)

Step2.

Simplify the equation (1) by dividing left and right sides by 2:

(1)

Solve it for

Step 3.

Substitute an expression for

(2)

or

Step 4.

Find the value of

Together with previously determined

All we have to do is to check that two other points specified in the problem lie on this graph.

Point

Point

So, the answer to this problem is