Question

HELP. Quadratic functions: How does the value of "b" affect the graph when a > 0 and when a < 0. Give an example.

Answer 1

This sort of problem is an "Exploration". You must ponder it, examine it, play with it, have a little fund with it, and gain some understanding. Try a few things and figure it out!

Graph these:

\(y = x^{2}\;;\;b = 0\)
\(y = x^{2} + x\;;\;b = 1\)
\(y = x^{2} + 2x\;;\;b = 2\)
\(y = x^{2} + 3x\;;\;b = 3\)
\(y = x^{2} - x\;;\;b = -1\)
\(y = x^{2} -2x\;;\;b = -2\)
\(y = x^{2} -3x\;;\;b = -3\)

You may wish to conclude that it would be more instructive in this form:

\(y = x^{2}\;;\;b = 0\)
\(y = (x+1/2)^{2} - 1/4\;;\;b = 1\)
\(y = (x+1)^{2} - 1\;;\;b = 2\)
\(y = (x+3/2)^{2} - 9/4\;;\;b = 3\)
\(y = (x-1/2)^{2} - 1/4\;;\;b = -1\)
\(y = (x-1)^{2} - 1\;;\;b = -2\)
\(y = (x-3/2)^{2} - 9/4\;;\;b = -3\)

Answer 2

The a value is the same in all these graphs. I know what you're saying though.

Answer 3

I tried it out with a function.
I think when a > 0, the vertex is on the negative side of the x axis, and when a < 0 the vertex is positive. Right?

Answer 4

You have it, but you did not mention the horizontal shift of the vertex. This is why the Vertex Form is useful. It shows the movement fo the Vertex in both directions.

@NY,NY

Answer 5

thanks :)