Key Equations

the quadratic formula $x=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$

The discriminant is defined as $b^2-4ac$

Key Concepts

• The zeros, or $x$-intercepts, are the points at which the parabola crosses the $x$-axis. The $y$-intercept is the point at which the parabola crosses the $y$–axis.
• The vertex can be found from an equation representing a quadratic function.
• A quadratic function’s minimum or maximum value is given by the $y$-value of the vertex.
• The minium or maximum value of a quadratic function can be used to determine the range of the function and to solve many kinds of real-world problems, including problems involving area and revenue.
• Some quadratic equations must be solved by using the quadratic formula.
• The vertex and the intercepts can be identified and interpreted to solve real-world problems.
• Some quadratic functions have complex roots.

Glossary

discriminant

the value under the radical in the quadratic formula, $b^2-4ac$, which tells whether the quadratic has real or complex roots

vertex

the point at which a parabola changes direction, corresponding to the minimum or maximum value of the quadratic function

vertex form of a quadratic function

another name for the standard form of a quadratic function

zeros

in a given function, the values of $x$ at which $y=0$, also called roots