Assignment 2:

Analysis of y = ax2 + bx + c

Presented by:

Amber Krug

y = ax2 + bx + c

Using the above equation, the problem asks to fix two of the values for a, b, and c and construct 5 graphs on the same axes as the third value varies.

LetŐs start by keeping a and b constant and vary c:

Below is the graph of

y = x2 + x + c where c = -8, -4, 0, 4, 8

From the graph, we see that the x-value of the vertex remains constant; however, the y-value of the vertex corresponds to the c-value.

Notice the shape and direction of each graph are the same.

Now, letŐs keep a and c constant and alter b:

Below is the graph of

y = x2 + bx + 1 where b = -6, -3, 0, 3, 6

From the graph, we see that the x-value and y-value of the vertex change, but the shape and direction of each parabola is the same.

Lastly, letŐs keep b and c constant and alter a:

Below is the graph of

y = ax2 + x + 1 where a = -2, -1, 0, 1, 2

a controls the direction of the graph.  When a is negative, the graph opens to the bottom, and when a is positive, the graph opens upward.  The shape of the graph changes with a as well.

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