# Lesson Shortcut in finding the vertex of any parabola

Algebra ->  Algebra  -> Quadratic-relations-and-conic-sections -> Lesson Shortcut in finding the vertex of any parabola      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Conic sections - ellipse, parabola, hyperbola Solvers Lessons Answers archive Quiz In Depth
 This Lesson (Shortcut in finding the vertex of any parabola) was created by by HyperBrain(694)  : View Source, ShowAbout HyperBrain: As I help you solve the problem, you are helping me practice my skills. Consider any parabola. A tangent of a curve is a line that passes through one point only(tangent means 'to touch') And, the vertex of any parabola is the point where the only HORIZONTAL LINE PASS THROUGH! The thing is, it requires DIFFERENTIATION! So, I'll teach you a basic differentiation rule commonly used in parabolas----The EXPONENT RULE! If , then, _______________________________________ This statement is read as follows: If y is defined as x raised to the power of n, then, the DIFFERENTIAL of y (written as y'), is x, raised to the power of n-1 and multiplied to n. ___________ Look at the equation above. The easy way to remember the differential is to write first dy/dx! ___________ Then from the equation , since n is the exponent, let's bring it down! ___________ Then, write x! ___________ Since n is already brought down, let's raise x to one less than n or . ___________ There, you're done! This is kinda hard to explain. I'll redefine it ONE MORE TIME! Example: Find dy/dx It is obvious that n=3. So, Yahoo! Now, no kiddin', we're going to apply it now. If a parabola is given to be, Before I can forget,dy/dx, in the equation represents the SLOPE OF THE CURVE in a given point Finding y', The DIFFERENTIAL OF A CONSTANT IS ZERO!!! Since the horizontal line has a SLOPE of zero, This means that the X-COORDINATE of the VERTEX is 1. If x=1,then, to find y, we refer to the original equation--- Thus, Therefore, the VERTEX calculated from the SHORTCUT is (1, 7) Wanna see a proof? Look below! Please watch our music video at http://www.metacafe.com/watch/1101445/science_avenue/ rate and leave a comment This lesson has been accessed 8902 times.