Key Concepts & Glossary
Key Equations
general form of a quadratic function | |
the quadratic formula | |
standard form of a quadratic function |
Key Concepts
- A polynomial function of degree two is called a quadratic function.
- The graph of a quadratic function is a parabola. A parabola is a U-shaped curve that can open either up or down.
- The axis of symmetry is the vertical line passing through the vertex. 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.
- Quadratic functions are often written in general form. Standard or vertex form is useful to easily identify the vertex of a parabola. Either form can be written from a graph.
- The vertex can be found from an equation representing a quadratic function.
- The domain of a quadratic function is all real numbers. The range varies with the function.
- A quadratic function’s minimum or maximum value is given by the y-value of the vertex.
- The minimum 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.
Glossary
- axis of symmetry
- a vertical line drawn through the vertex of a parabola around which the parabola is symmetric; it is defined by
- general form of a quadratic function
- the function that describes a parabola, written in the form where a, b, and c are real numbers and
- standard form of a quadratic function
- the function that describes a parabola, written in the form where is the vertex.
- 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