Difference Between Linear and Quadratic

Decimals and fractions are mathematical models that can allow simplifying quite a lot of different types of equations.

Linear vs Quadratic

The main 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 vs Quadratic

Moreover, a linear function is a contrast to exponential functions where the rate of change increases over time.

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.

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.

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.

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.

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 are commonly seen in physics because they model simple situations that have large changes in the outcome based on small changes in the input.

This is just a Quadratic function example where the Quadratic function bears repeating of the y-axis and x-axis cross at the origin.

The discriminant of a Quadratic function is the square root of the discriminant of the linear function.

Main Differences Between Linear and Quadratic

  1. Graphical representation of a Linear function is mostly through a Straight line, whereas Graphical representation of a Quadratic function is mostly through a parabola.
  2. 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.
Difference Between Linear and Quadratic

Conclusion

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.

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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