Quadratic inequalities

• Quadratic inequalities are a type of algebraic inequality that involves quadratic expressions. A quadratic inequality looks like ax2+bx+c>0, ax2+bx+c<0, ax2+bx+c≥0 or ax2+bx+c≤, where a, b, and c are constants, and a≠0.
• The graph of the quadratic function f(x)=ax^2+bx+c is called parabola
• A quadratic equation can be written as an equivalent quadratic inequality by replacing the equal sign with either greater than or less than signs.
• To solve a quadratic inequality, we need to find all values of x such that the inequality holds true.
• If the coefficient of x^2 is positive, then the parabola opens upward; if it's negative, then the parabola opens downward.
• We use the same steps to solve quadratic equations when solving quadratic inequalities.
• When finding solutions to quadratic inequalities, there may be no real number solution, one real number solution, or two real number solutions.
• When solving quadratic inequalities, we use the same steps as when finding solutions to quadratic equations, but instead of setting the expression inside the parentheses equal to zero, we set it greater than or less than zero depending on whether the original inequality has a "greater than" or "less than" symbol.
• When solving quadratic equations, there may be no real solutions, one real solution, or two real solutions.
• We can also use the vertex form y=a(x-h)^2+k to determine the range of values for which the inequality is satisfied.
• In general, when finding the roots of a quadratic equation, we use the quadratic formula: x = (-b ± sqrt(b² - 4ac)) / 2a.
• In some cases, the discriminant will be zero, indicating that both roots are identical.
• For quadratic functions, the vertex represents the lowest point on the curve, while the axis of symmetry divides the parabola into left and right halves.