The Department of Mathematics Education


Investigation of the Graphs of Quadratic Formula

by GooYeon Kim

 


Let's consider the quadratic formula

By using Graphing Calculator, we can graph the above formula.

 

First, we are replacing each x by (x-4) and drawing a graph. Then we get a new formula,

According to this formula, we have

Now, let's overlay these two formulas.

 

Next, change the equation with different coefficients.

 

Now, let's think about what will happen if we change the constant and second quadrant.

 

Again, change the second quadrant.

 

If we would like to get a graph concave down, what should we change? We explored graphs by changing coefficients of the given quadratic equation except the one of second degree of x. Then we have to try this.

Then the graphs of above equations are following:

However, we don't get what we want, that is, concave down. Now, try again.

Finally, we can see the concave down graphs of given equations.

 


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