1) Quadratic inequality:

A quadratic inequality has the same characteristics as a second-degree equation, except that in place of the equal sign there is an inequality symbol. The standard form of the inequality has all terms on the left side of the inequality symbol with only 0 on the right. 

2) What is the difference between a
linear inequality and a quadratic inequality? 

Equations: Linear equations are in the form y=mx+b, where quadratic equations have a variable that is squared, so they are in the form y=ax^2+bx+c 

Graphs: The Graph of a linear equation on a x-y coordinate plane is a straight line. A quadratic equation results in a graph shaped like a parabola

Slope: A common task with linear equations is finding the line’s slope, which is equal to m in the equation y=mx+b. A quadratic equation’s slope is always changing because the parabola is curved. 

Solving: Linear equations only require simple algebra of adding, subtracting, multiplying and dividing, more complicated processes of factoring, finding square roots or using the quadratic formula solve quadratic equations. 

Solutions: When given a y value, a linear equation will result in only one solution for an x value. A quadratic equation can have two solutions for x when given a y value. 

3) Determine how to solve a
quadratic inequality with steps:

1. If necessary, first rewrite the inequality in standard form; that is put all the terms on the left side with only 0 remaining on the right side of the inequality symbol. 

2. Let y= the algebraic expression on
the left side of the inequality symbol, resulting in a quadratic equation. 

3. Find the x-intercepts by solving 0=ax^2+bx+c and do a sketch of the quadratic equation showing only the intercept(s). There is no need to locate the vertex or any extra points. 

4. By inspection of the graph, determine the answer of the inequality.  

4) Example:  

Solve: x^2-2x-3<0 

0 = x^2-2x-3

0 = (x+1)(x-3) 

x = -1 or x = 3

Since a=1 is positive, curve opens
up. 

The y-intercept is c=-3 

The x-intercepts are -1 and 3 

References:Web: 

May, K. (2009). Differences Between Quadratic & Linear Equations. Retrieved from: http://www.ehow.com/facts_5483849_differences-between-quadratic-linear-equations.html

Book:
Lee Bleau, B. (2003). Solving Quadratic Inequalities. In Forgotten Algebra (Third ed.). Hauppauge, New York: BARRONS.

 find out if it is greater that zero or l

a)A Quadratic equation in standard form is this: ax^2 + bx + c = 0

Inequalities have the following symbols: >, <, ≤, ≥

b)therefore quadratic inequalities look like this: 3x^2 + 4x + 2 < 0 

c)We solve these inequalities by finding intervals. 

first you find the =0 points

and in between those =0 points there are intervals that are greater than zero or less than zero

then you use a test value to

less than zero

d)example: 

Solving Quadratic Inequalities (Solving Quadratic Inequalities)

http://www.mathsisfun.com/algebra/inequality-quadratic-solving.htmlKanold, L. (1993). Graphing Quadratic Inequalities. In 

Algebra 1. Heath and Company.

REFERENCES

References:

Website: 

May, K. (2009). Differences Between Quadratic & Linear Equations. Retrieved from:http://www.ehow.com/facts_5483849_differences-between-quadratic-linear-equations.html

Book:

Runde, A. (n.d.). Chapter 8 Quadratic Equations. In <i>Intermediate Algebra For Collage Students</i> (8th ed., p. 703). Pearson Education.

D.

(FOURTH IMAGE, RIGHT) Determine the intervals that fulfills the inequality conditionsThen the solution is clearly:x < –2 or x > 2You could have multiplied the initial inequality through by –1, giving  "x2 – 4 > 0". The zeroes would have been the same: x = –2 and x = 2. But this parabola would have been right-side-up, since the quadratic would have been "positive". That's okay though, because, by multiplying through by –1,  you would have flipped the inequality, so you would have been looking for where the quadratic is greater than zero. Since the parabola would have been right-side-up, the graph would have been above the axes on the ends; so the solution would have worked out to be the same as before: x < –2 or x > 2:(FIFTH IMAGE)   |   REFERENCES.

(n.d.). Retrieved March 24, 2015, from http://study.com/academy/lesson/graphing-and-solving-quadratic-inequalities.html

Solving Quadratic Inequalities: More Examples. (n.d.). Retrieved March 24, 2015, from http://www.purplemath.com/modules/ineqquad3.htm

Urban, P., Martin, D., Haese, R., Haese, S., Haese, M., & Humphries, M. (2008). Quadratic Equations and Functions. In Mathematics (Second ed., p. 935). Haese & Harris Publications.

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