3.1: Quadratic Functions
- Page ID
- 203402
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- Solving Absolute Value Equations
- Quadratic Functions
- Vertex Form and Completing the Square
Recognizing Characteristics of Parabolas
The shape in the following figure is called a parabola. Every parabola has one extreme point called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the parabola. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value. In either case, the vertex is a turning point on the graph. The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry. These features are illustrated in following figure.
Quadratic Functions in General Form
Quadratic Functions in Standard Form
Write the equation of the graph from MyOpenMath \( \PageIndex{9}\).
Rewrite the quadratic function \( f(x) = -3x^2 + 6x - 2 \) in standard (vertex) form by Completing the Square.