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:
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Then if a=1 and b=1, c takes values
from -4 to 4, the equation is
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Where does
the parabola cut the y-axe? |
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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. |
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Now, we will fix a=1, b=-1 and c
varies from -4 to 4. |
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Where does
the parabola cut the y-axe? |
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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. |
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Summary |
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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. |
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Now you can see the animation |
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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. |
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Summary |
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Consider the equation
If I complete square I get 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. |
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Note: All graphs of this webpage were made with
Graphing Calculator 4.0 |