1 Answer

Farhad Sakhaei · Answer 1 · 2023-09-26T22:16:44+0000

We will investigate how to construct an equation of a parabola given three points.

A parabola is described as a polynomial relationship of highest order 2. The general equation of a parabola is given as follows:

$y=ax^2\text{ + bx + c}$

Where,

$a\text{ , b , and c are constants}$

To determine the values of these constants we will utilize a set of pair off coordinates given as follows:

$(\text{ -1 , 14 ) , ( 0 , 7 ) , ( 1 , 6 )}$

The process off evaluating the three constants ( a,b, and c ) is to plug in the respective coordinates in the general form of a parabolic function. Then develop a system of equations which can be solved simultaneously.

Using the pair ( 0 , 7 ). We will plug in the respective coordinates in the general form and evaluate:

$\begin{gathered} 7\text{ = a}\cdot(0)^2\text{ + b}\cdot(0)\text{ + c} \\ c\text{ = 7} \end{gathered}$

Taking the pairs ( -1 , 14 ) and ( 1 , 6 ). We get a pair of equations as follows:

$\begin{gathered} 14\text{ = a}\cdot(-1)^2+b\cdot(-1)\text{ + 7} \\ 7\text{ = a - b }\ldots\text{ Eq1} \\ \\ 6\text{ = a}\cdot(1)^2+b\cdot(1)\text{ + 7} \\ -1\text{ = a + b }\ldots\text{ Eq2} \end{gathered}$

Now once we have developed a system of linear equations. We will solve them simultaneously by elimination: