Solving Quadratic Equations
A quadratic equation is an equation of the second degree, meaning that for an equation in
x, the greatest exponent on x is 2. Quadratics most commonly refer to vertically oriented
parabolas—that is, parabolas that open upward or downward. The graph of a vertically oriented
parabola has the shape of a rounded "v," and the bottommost (or topmost) point is called the
vertex. The equation for a parabola is usually written in either standard or vertex form; however,
the standard form is more commonly used to solve for the xintercepts, or roots. The standard
form is y = ax2+ bx + c for any real numbers a, b, c where a ≠ 0. The vertex form is y  k = a(x 
b)2 with vertex (b, k) and where a ≠ 0. Because xintercepts are the points at which the graph
crosses the xaxis, the solutions are always found by substituting 0 for y. The roots are often
useful in solving real world problems, and there are three common ways to find the roots:
factoring, using the quadratic formula, and completing the square.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 ritzel
 Quadratic Formula, Vertex Form, Quadratic equation, Elementary algebra

Click to edit the document details