# How do you write an equation of the quadratic function whose graph contains the points (-4,-57), (2, 39), (5, 168)?

##### 2 Answers

#### Explanation:

General form of a quadratic equation is

So for the given points, we have

[1]

[2]

[3]

Simplifying these:

[3]

[4]

[5]

Subtracting [4] from [3]

[6]

Subtracting [4] from [5]

[7]

Multiplying [7] by 2

[8]

Adding [6] and [8]

[9]

Dividing [9] by 3

[10]

Substituting

[11]

Simplifying

[12]

Dividing [12] by

[13]

Substituting

[14]

Simplifying

[15]

[16]

#### Explanation:

First, we will create three equations, one for each point. It will be in the general form

**First Equation from P(-4,-57)**

**Second Equation from P(2,39)**

**Third Equation from P(5,168)**

**System of Equations:**

Now, we can solve for the values of

*Fourth Equation taken from the first and second equations:*

We will first get the value of

Let's simplify this to:

*Fifth Equation taken from the first and third equations:*

We will substitute the value of

Let's simplify this to:

**Solution**

Now, we will use the 4th and 5th equation to solve for

To solve for

So the values of

Finally, to get the quadratic equation, just substitute the values of