**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.