For this week’s Portfolio Problem, I chose to work on the Identical Quadratics situation. This problem tasked me to fill in blank spaces in order to create three equation that would result in the same parabola. To fill in the blanks, I could only use whole numbers between 0 and 9, and I could only use each number one time.

The first step I took to solve this problem was filling in one of the equations. I started by putting 2 and 3 into the blank spaces of the second equation. Then I used the method of completing the square to determine what values belonged in the third equation. I learned that if I used 2 and 3 in the second equation, then the only values that would fit in the third equation would be 5 and 5. Although, this would not work because I can only use each number once. I restarted and tried plugging 2 and 4 into the second equation, and then using the method of completing the square to find values for the third equation. This resulted in y = (x + 2)(x + 4) and y = x^2 + 6x + 8.

Once I had the second and third equations, I just had to solve for the first one. Originally, I had started plugging the remaining numbers in, but then I realized that this equation was vertex form. Then I simply put 3 and 1 into the remaining spaces. When I graphed all three equations at once, they had the same parabola!

 

Throughout this problem, I learned more about the forms of quadratic equations and reviewed the concept of Quadratic Functions. I look forward to completing another Portfolio Problem soon!