Quadratic Equations

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Graphing Form and Standard Form As you have worked with quadratic functions, equations, and expressions you have regularly seen two forms. One is known as graphing (or vertex) form, the other is known as standard form.

A quadratic equation in GRAPHING or VERTEX FORM looks like:

Y = a(x–h)² + k.

- the vertex is (h,k) and the axis of symmetry is the line x=h.
- the parabola opens up when a is positive and opens down when a is negative.
- if |a| > 1, the graph will be narrower than the graph of y = x²

- if |a| <1, the graph will be wider than the graph of y = x^ 2

For example, the equation Y = 3(x–1)² – 5 is in graphing form where a = 3, h = 1, and k = –5.

The following quadratic equation represents the same parabola as y = 3(x – 1)² – 5, but it is written in what is generally called standard form. For y = 3x² – 6x – 2, a = 3, b = –6, and c = –2.

A quadratic equation in STANDARD FORM is written as y = ax² + bx + c.

The vertex of a parabola locates its position on the axes. The vertex serves as LOCATOR POINT for a parabola. The other shapes we will be investigating in this course also have locator points. These points have different names but the same purpose for each different type of graph.