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Given vertex and a point
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Given vertex and a point

Converting the vertex form to standard quadratic form is useful in determining the difference between the y-intercept between two quadratic functions



Parabola minimum or maximum = ( , )

and a point on its curve. = ( , )


ANSWER: The derive quadratic equation in standard form is shown below and calculated automatically. The explanation on how to solve for value of "a" , "b", and "c" is also shown below. Notice it obeys the formula and therefore are repeatable and can be done faster using your phone, tablet, laptop or desktop computer.

= a 2 + b + c ANSWER: This is the derived quadratic equation

Now use the above derived equation to predict the value of y(x) ? when x =
Answer y(x) = This is a simple explanation how machine learning works. The computer algorithm will do trial and error until it discover the generalized equation that is true or valid. Trained human expert like mathematician and theoretical physicist only need two or three training data and be able to derive the quadratic or parabolic equation. Then use it for prediction. This example is a preview that human intelligent + artificial intelligence will speed up calculation that will lead to work productivity and more discovery in the future.


Solving the value of by using vertex form and substitute the value of it's vertex and the given point.

= a ( x - h ) 2 + k

+ =

=


Solving the value of

= - b * 2 a

=

Solving the value of

= k + 2 b 2 / 4 a

=





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