Rayen Antillanca. Assignment 2

Fix the values for a and b, vary c. Make at least 5 graphs on the same axes as you vary c. For the general function of the parabola, namely:

 Then if a=1 and b=1, c takes values from -4 to 4, the equation is Where does the parabola cut the y-axe? As you can see, the parabola keeps the shape but it moves over the y-axe. The value of b=1 indicates that the vertex of the parabola has a translation to the left of the origin. Also, it means, the parabola makes a translation depend on the value of c. In this case, as c is positive, the cut of the parabola in the y-axe is in the positive side, and when c is negative, the cut happen in the negative side of the y-axe.

 Now, we will fix a=1, b=-1 and c varies from -4 to 4. Where does the parabola cut the y-axe? As you can see, the parabola keeps the shape but it moves over the y-axe. The value of b=-1 indicates that the vertex of the parabola has a translation to the right of the origin. Also, it means, the parabola makes a translation depend on the value of c. In this case, as c is positive, the cut of the parabola in the y-axe is in the positive side, and when c is negative, the cut happen in the negative side of the y-axe.

 Summary C is the value where the parabola cuts the y-axe. When c is a negative number, the parabola cuts in that negative number in the y-axe. When c is a positive number the parabola cuts in that positive number in the y-axe. When c=0 the parabola cuts in zero the y-axe of Cartesian plane.

 Now you can see the animation As you can see in the prior animation, when the c varies from -4 to 4 the parabola moves through the y-axis. This implies a translation of the parabola. Recall, a translation means to move every point of the parabola, in this case a constant distance in a specific direction.

 Summary Consider the equation If I complete square I get  then the vertex of this parabola is moved  from the origin to the right, and it is moved upward  from the origin. As you know, when c=0 the parabola cuts the y-axe in the origin. Then, if we vary c, we can see that this function is the same parabola, but the parabola is moved upward or downward depend of the value of c.

 Note: All graphs of this webpage were made with Graphing Calculator 4.0