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