Solving Quadratic Equations and Inequalities

Vocabulary

completing the square

process used to rewrite a quadratic expression as the sum of a perfect square trinomial and a constant

discriminant

part of the quadratic formula that is under the radical sign:
b24acb^2-4ac

factoring

process of writing a number or algebraic expression as a product

quadratic equation

polynomial equation, where aa, bb, and cc are real numbers and a0a\neq 0, that can be written in the form:
ax2+bx+c=0ax^2 + bx + c = 0

quadratic formula

formula used to solve a quadratic equation of the form ax2+bx+c=0ax^2+bx+c=0 by using its coefficients:
x=b±b24ac2ax=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}

quadratic inequality

mathematical statement that compares a quadratic expression of the form ax2+bx+cax^2 +bx + c to another expression or value using the symbols <<, >>, \leq, or \geq

solution of an equation

value of the variable that makes the equation true, which means both sides are equal

solution of an inequality

value of the variable that makes the inequality true, which means the comparison is valid

x-intercept

value of xx where a graph touches or crosses the xx-axis

zero of a function

any input value of a function that makes the output of the function equal to zero