Will Clark and Matt Akins

--The "human quatratic" created by the gifted Matthew (left) and Will (right)--

Quadratic Forms
Standard Form -- 

 

Each letter represents a certain aspect about the graph or equation that it is related with. The Standard Form is composed of A, B, and C variables: A= Wideness of parabola  (- makes upside down) B= Left/Right and down when A= + C= y-intercept Now we will explain how to find the standard equation when given either the intercept or vertex equation. In creating the STANDARD form when given the INTERCEPT form, here are transition equations. A is equal to A B is found by taking  -(A*P+A*Q) C is found by multiplying A*P*Q Once you have gotten A,B, and C you only have to place these numbers into their respective areas in the equation! When given the VERTEX form, here is how to find the STANDARD form. A is equal to A B is found by multiplying   -2*A*H C can be found by multiplying  A*H2+K Once again, now you simply have to put what you have found into the Standard equation.

Vertex Form -- 

 

The Vertex form is made up of A, H, and K variables, each variable represents a certain aspect on the graph: A= same in all three equations H= x coordinate of maximum/minimum K= y coordinate of maximum/minimum In finding the maximum or minimum of the graph, a TI calculator is helpful.  You simply search for the max or min and the calculator gives you both the x and y coordinates.  The name of this form in itself should lend you to the solution.  The vertex of the parabola is the defining feature of the graph in finding the full equation.  H and K are very important for the vertex form. Here is the transfer route for finding the VERTEX equation when given the STANDARD equation. A is equal to A H is found by taking   B/-(2*A) K is found by taking  C-A*H2 To find the INTERCEPT form when given the VERTEX form, you must take a two step process.  First you have to change it to the standard equation.  (This is given above).  After you have the standard form of the equation, you must change the standard to vertex.  This will be explained following the introduction to the Intercept form.

 

Intercept Form -- 

The Intercept form is composed of A, P, and Q variables.  Each one of these variables represents a key part to the graph which is necessary in finding the equation.  The variables are as follows: A= same as all A P= solution for one zero (Point at which the parabola crosses the X-axis) Q= solution for second zero (Second point at which the parabola crosses the X-axis) To find the the INTERCEPT form when given the STANDARD form, follow these steps below: A is equal to A P is a long one.  It is found by taking  -B+ or - the square root of B2-4*A*C/2*A.  This is the quadratic formula!  How crazy. I wonder why it was named that?!?!?! Q is found by taking  C/A*P Now, back to what was mentioned above in the Vertex section.  To find the INTERCEPT when given the VERTEX form, you have to transfer the Vertex into the Standard form, like earlier mentioned.  But then the second step comes next.  This step involves transfering the Standard form into the Intercept form.  This can be achieved by following the simple steps above.  After completing this two step process, you have successfully found the Intercept form when given the Vertex!

 

Now, Snika and Dub would like to share with you some very important web pages.  The pages are in some way related to this site, and we hope that you enjoyed our page.  Hopefully you will leave smarter than you came!  Happy surfing............. Mr. Youngs Crazy Page of PreCalculus Fayetteville High School History of Quadratics A Few Quadratics to Test Your Ability An Algebra Site to Explore An Interestinc Projectile Motion Page (Fun to Play with) Will's E-Mail Matt's E-Mail Our Teacher, D.A.Y.'s E-Mail