Investigating the Parabola


John R. Simmons


The graphs of quadratic functions of the form as the one below is investigated in this assignment.



As can be seen from the three graphs above, when the value of a is increased the graph of the curve narrows.




And when a is a negative number, the graph of the curve opens downward and narrows as the absolute value of the negative increases.




When b is positive and increasing the graph of the curve shifts in a circular motion from right to left. When b is negative and decreasing, the graph of the curve shifts in a circular motion from left to right.


This is graph of 5 parabolas with a and b held constant and c varying.


As c varies, the graph of the parabola is shifted along the y axis.

The graphical representation of the quadratic equation can help in analyzing the roots of the equation. The points on the intersection of the curve with the x-axis determine the zeroes of the function--which are the roots when the roots are real. When the curve is tangent to the x-axis, a double root occurs. And, when quadratic equation has no point on the x-axis, the roots are imaginary.

Click here to see the animation.


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