Christa Marie Nathe Parabola Shifts
In this investigation we are going to construct a series of graphs based on the equation y=ax2 + bx + c. There will be different values for a, b and c which are any rational number. The first set of graphs reflects the following equations where the value for a is varied, while the others remain constant.
It is obvious from the graph that when the value for a changes, the graph is altered. As the value for a increases, the parabola becomes thinner than its predecessor. If the values for a are negative the parabolas are reflected over the x-axis.
The following graphs reflects the various values of b, while a and c are kept constant. The graph expands as the value of b increases and interestingly pulls to the left. We can expect that if the values for b were negative that the parabola would expand, but pull to the right. As we observe, this is the case.
y=x2+2x+3 y=x2+2x+3 y=x2+2x+3 y=x2+2x+3 y=x2-2x+3 y=x2-2x+3 y=x2-2x+3 y=x2-2x+3
Now we will look at the graphs of the equation where the value for c is changed, both positive and negative. As you have observed from the previous graphs, it would seem that the c value anchors the graph to a y-intercept. As we change c, while a and b remain constant one could predict the shifts of the graphs.
y=x2+2x-3 y=x2+2x-4 y=x2+2x-5 y=x2+2x-6 y=x2+2x+3 y=x2+2x+4 y=x2+2x+5 y=x2+2x+6
As we have observed in this investigation, the coefficients a, b and c have direct bearing on the graph. Realizing these implications allows one to understand the functions of the quadric equation.