by

SOMIN KIM

Examine graphs for the parabola for different values of coefficients.

Fix two of the vales for a, b, and c.

(Make at least 5 graphs on the same axes as you vary the third value.)

1. I will fix a and b, then change value of c.

The graphs are moved by value of c. Value of c decides the graph's y-intercept.

2. I will fix b and c, then change value of a.

Because value of c which decides y-intercept is fixed as 1, all graphs are meet (0,1).

If value of a is changed, the curve of graphs is changed.

When the value of a is positive integer, the graph is concave.

When the value of a is negative integer, the graph is convex.

As is getting bigger, the slope of graph is steep.

If a=0, the equation becomes a linear equation.

3. I will fix a and c, then change value of b.

Because value of c which decides y-intercept is fixed as 1, all graphs are meet (0,1).

If value of b is changed, an apex of graphs is changed.

When the value of b is positive integer, an apex of graph is on quadrant I.

When the value of b is negative integer, an apex of graph is on quadrant II.

If b=0, an apex of graph is on y-axis.

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