Anne Wacker

2021-12-27

Why given two points are there only one exponential equation, one linear equation, but infinitely many quadratics?

trisanualb6

Step 1
The generalized forms of exponential and linear equations are:
$y=a{e}^{bx}$
$y=mx+c$
Step 2
Observe that there are two arbitrary constants, a and b in the exponential equation and similarly there are two arbitrary constants, m and c in the linear equation. Thus given any two solution points of these equations, a unique function can be defined.
Step 3
The generalized form of quadratic equation is:
$y=a{x}^{2}+bx+c$
Step 4
Since this equation has three arbitrary constants, a, b and c we need at least three solution points to find a unique quadratic function satisfying these points.
Step 5
If only two points are given then at the best, one can only find values of two arbitrary constants and the third arbitrary constant is free to take up all the real number values.
This means there are infinitely many possible quadratic equations that can be defined for each separate value of the third arbitrary constant.
Therefore, given two points, there is only one exponential equation, one linear equation, but infinitely many quadratics possible.

Buck Henry

Step 1
This is first of all not a truth. We must first of all clear this confusion.
A quadratic equation is the one whose highest degree in its variables is 2. Quadratic equation term is generally used for relative.
Examples? Let us consider ${x}^{2}+3xy+5=0$. This u notice has two variables x and y. But we say that this is a quadratic equation with respect to x. Got my point? In respect to y, it is only a linear equation.
We now define linear equation.
A linear equation relative to any of its variables is an equation in which the highest power of the selected variable is 1.
It is that only two variables linear equation are in course and quadratic equation in one variable in th 10th one. You must know that any polynominal could have many variables.

user_27qwe

Step 1
$2x+3=0$
Isn't this a linear equation? Just look,it has only one variable.
${x}^{2}+{y}^{2}=1$
Isn't this a quadratic equation? Just look ,it has two variables.
Bro there's nothing like that linear equation will have this much variable and quadratic equation will have this much.Actually we can classify equations on both this basis.
On the basis of degree
Check for the highest power in variable.If it is one, we call it linear and if it is two we call it quadratic.
On the basis of no of variables. If it has just one variable (x or y or z or anything) we call it one variable.And if it has more than one then we call it two variable or three variable accordingly.
Let me give you some example.
$2x+3=0$, this is a linear equation in one variable
$2x+3y=7$, this is a linear equation in two variable
${x}^{2}+2x-7=0$, this is a quadratic equation in one variable
${x}^{2}+{y}^{2}=36$ this is a quadratic equation in two variable
${x}^{2}+{y}^{4}+z=11$