

How Solve a Quadratic Inequalityquadratic inequalties the graph of a quadratic inequality  how to solve & graph quadratic inequalties
Before learning how to solve the equation of a quadratic inequality.
It is important that you 1)can graph parabolas 2) understand the vertex and standard form equation of a parabola 3) solve quadratic equations
Quick review of the graphs and equations of linear inequalities.
The graphs of quadratic inequalities follow the same general relationship. Greater than inequalities are the region above the equation's graph and less than inequalities are made up by the region underneath the graph of the equation. What is the solution of a quadratic inequality?In the end, you can use a pretty straight forward formula to solve quadratic inequalities. First, it's important to try to understand what a quadratic inequality is and also to remember what the solution of a quadratic equation is.Steps to solve a quadratic inequality
Let's examine the graph of the quadratic inequality, y > X² − 1
The solution is all points on the xaxis between 1 and 1.
y < X² − 1
See Graphs side by side (Easier to compare graphs)
A closer look at Y > X² − 1
When we are trying to calculate the solution of a quadratic inequality Y > X² − 1. We want to find all values of x for which y =0 & Y > X² − 1.
A closer look at Y < X² − 1
When we are trying to calculate the solution of a quadratic inequality Y < X² − 1. We want to find all values of x for which y =0 & Y < X² − 1.
General Formula for Solutions of Quadratic InequalitiesThe table below represents two general formulas that express the solution of a quadratic inequality of a parabola that opens upwards (ie a > 0) whose roots are r_{1} and r_{2}.
We can reproduce these general formula for inequalities that include the quadratic itself (ie ≥ and ≤)
Warning about imaginary solutions: Although the solution of a quadratic equation could be imaginary The solution of a quadratic inequality cannot include imaginary numbersthis is becuase imaginary numbers cannot be ordered. Practice: How to graph and solve a quadratic inequality 