Difference Between Linear and Quadratic (with Table)

Decimals and fractions are mathematical models that can allow simplifying quite a lot of different types of equations. However, Linear and Quadratic functions are quite a bit more difficult to solve, but both Linear and Quadratic can be solved using Linear and Quadratic formulas. Linear and Quadratic are indistinguishable, yet they are dissimilar from each other.

Linear vs Quadratic

The difference between Linear and Quadratic is that Linear is an equation that is just a straight line on the graph with a degree of one that can be written in symbolic or graphical form using x and y coordinates. Quadratic, on the other hand, is not just a straight line on the graph but a parabola, moreover, with a degree of two that are written in symbolic and graphical form using x and y coordinates.

Linear functions can be used in many different ways for various things. Moreover, a linear function is a contrast to exponential functions where the rate of change increases over time. For example, y = 2x + 3 is a linear function because when x increases by 1, y will increase by 2 and then 3 when x increases by 2 and so on and forth.

Quadratic functions are well-known as the ratio of two squared variables. Moreover, there are 5 types of quadratic functions. Quadratic functions are mostly graphically represented as parabolic forms that are often seen in physics and mathematics with a degree of two that are written in symbolic and graphical form using x and y coordinates.

Comparison Table Between Linear and Quadratic

Parameters of ComparisonLinearQuadratic
DefenitionA linear function is a contrast to exponential functions where the rate of change increases over time.Quadratic functions are defined as the ratio of two squared variables.
DegreeDegree of one.Degree of two.
RepresentationIt is represented as Ax+By+C=0It is represented as Ax²+By+c=0 
Graphical RepresentationStraight line.Parabola.
Example 1x+4=7, 3x+2=3, 7x=11, x + 3=4y = x 2, 5x²+3x+2=0, x² +4x+5=0

What is Linear?

Linear are equations that have only one variable of the form ax + by = c. These linear equations can be written in symbolic or graphical form using x and y coordinates where x and y are variables. Symbolic forms of linear equations are called matrix form or general form, or determinant form. This method works best for any number of variables and complex numbers.

Sometimes a linear equation is called if it has certain properties. The first property is that two variables are equal to each other or are constant. The second property is that one variable can be represented by a linear function of the other variable. The third property is that the left-hand side of an equation equals zero. Some examples of equations are 1x+4=7, 3x+2=3, 5+4x=6 etc.

Another example would be finding the equation of a line in two ways. The first way that minimizes the distance from the point of origin and the point on the graph that you wish to find is to use linear functions. This is called graphing a line by hand.

A linear equation is a type of equation that can be written in the form ” a(x+b) = c.” For example, x + 3=4, 3x+2=3, 7x=11 etc or e.g. y=x. The first two examples are pretty simple. Moreover, the second example represents that a linear equation is just a straight line on the graph with a degree of one.

What is Quadratic?

Quadratic functions are quite a bit more difficult than other functions found in mathematics. The only way to solve them is to use a quadratic formula or work it out with a calculator or by hand carefully. Quadratic functions may sometimes sound like a nightmare. However, it’s not that difficult once you know how to solve them easily with Quadratic formulas.

Quadratic functions are commonly seen in physics because they model simple situations that have large changes in the outcome based on small changes in the input. For example, air resistance or force exerted by liquids can be modeled by quadratic functions. Vertex Form is a type of Quadratic function that has a negative coefficient in front of the square root term. For example -b x -4(x-1)(x-2)(x+3)(x+4).

For example, Quadratic functions of ( e . g . y = x 2) The y-axis is on the left, and it’s made up of two lines, one horizontal and one vertical. The first one goes down and to the right and the second up and to the left. Both of these lines intersect at the origin where the two axes cross. This is just a Quadratic function example where the Quadratic function bears repeating of the y-axis and x-axis cross at the origin.

Quadratic functions are defined as the ratio of two squared variables. The variable can take on any positive real number value. The discriminant of a Quadratic function is the square root of the discriminant of the linear function. So, for example, if you make a graph of an equation with a slope of 1.5, then the discriminant is 2/1.5 = 0.75 because each side of that equation is squared to be 1.5, giving 1.5 squared is 2, which is the discriminant.

Main Differences Between Linear and Quadratic

  1. A linear function is a contrast to exponential functions where the rate of change increases over time, whereas, Quadratic functions are defined as the ratio of two squared variables.
  2. Linear is found to have a degree of one, whereas Quadratic is found to have a degree or two.
  3. Linear functions are represented as Ax+By+C=0, whereas Quadratic is represented as Ax²+By+c=0.
  4. Graphical representation of a Linear function is mostly through a Straight line, whereas Graphical representation of a Quadratic function is mostly through a parabola.
  5. Examples of Linear functions are 1x+4=7, 3x+2=3, 7x=11, x + 3=4 , whereas Examples of Quadratic functions are y= x 2, 5x²+3x+2=0, x² +4x+5=0.

Conclusion

Mathematical equations are expressed as Linear functions and Quadratic functions to meet certain criteria. Moreover, these types of functions are commonly seen in physics and mathematics. Quadratic functions are defined as the ratio of two squared variables with a degree of two. For instance, air resistance or force exerted by liquids can be modeled by Quadratic functions.

Linear functions can be used in many different ways for various things. For example, economists often use linear functions to represent consumer demand on a graph, where if x represents income and y represents demand, then y = ax + b. This equation demonstrates how consumers will demand a certain amount of a specific good, but only when the income they have is relatively high.

References

  1. https://arxiv.org/abs/1906.02590
  2. https://scripts.iucr.org/cgi-bin/paper?a12813
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