Becky Dragan

Assignment 2

Below is a graph of for c = 4, 1, 0, -1, and -4.


Notice that changing c causes a vertical shift in the parabola.

What does c tell us about the y-intercept of the parabola?


Below is a graph for different values of a in the equation .

black: a=0.22, purple: a=0.5, red: a=1, blue: a=4, gray: a=-1, yellow: =0.5, green: a=-0.22, light blue: a=-4

What happens to the shape of the graph as a changes?

How does varying a change the minimum value of the parabola?

Why do all the parabolas have a common point?

What do you think would happen if a was 0? Click here to see if your guess was correct.


Below is a graph of for different values of b.

red: b=4, blue: b=2, green: b=1, purple: b=0, light blue: b=-1, yellow: b=-2, gray: b=-4

How does changing b change the vertex of the parabola?

Is there a vertical shift in the parabola? A horizontal shift?

What point in common do the different parabolas have? Why?



Below are several graphs for different values of d in the equation


gray: d=-6, yellow: d=-3, green: d=-1, purple: d=0, red: d= 1, blue: d=3, light blue: d=6

Does varying d appear to change the shape of the graph?

What happens to the x-intercepts as d varies?

Do you see a correlation between d and the vertex of the graph?

Notice that above when we changed the value of a in , it caused a vertical shift in the parabola. Now when we change the value of d in , it caused a horizontal shift in the parabola.