Effect of changing the value of a,b,c in quadratic equation

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Visualization is important for students and teachers alike, if they want to understand how altering different constant in a quadratic equation is going to change the appearance of the graph. By understanding how different constant alteration is going to affect on the position and shape of the graph, we can explain why certain quadratic equation have two, one or no real root. It is also important if we want to understand the meaning of quadratic equation discriminant. For the explanation below, we assume that the constants refer to quadratic function in the form of y = ax2 + bx + c. Note that in graphs below, the red horizontal line is the x-axis.

The effect of altering the value of a-constant

QuadAA.png

Altering the value of the constant a is going to affect the shape of our quadratic function. If we assign higher value for a, our graph is going to become thiner and thiner. In the other hand, assigning lower value of a is going to make the graph wider. As could be observed in the graphs above the graph for quadratic function with a-value of 0.25 is wider than quadratic function with a-value of 0.5, 1 and 2.

The effect of altering the value of b-constant

QuadBB.png

Altering the value of b constant is going to affect the position of x-intercept of the graph. This alteration is not going to affect the shape of our quadratic function graph. By changing the value of b, the position of one of the x-intercept is going to be translated by -b/a to the direction of x.

The effect of altering the value of c-constant

QuadCC.png

Altering the value of c-constant is going to affect the position of the entire graph. This alteration is not going to have any effect on the shape of the graph. As shown in the images above, changing the value of c-constant is going to move the entire graph along the y-axis.

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