Question 213552: how can i telln if a graph opens up or down by looking at the equation Found 2 solutions by rapaljer, drj:Answer by rapaljer(4671) (Show Source):
You can put this solution on YOUR website! If you are talking about a parabola like y=x^2, the if the coefficient of x^2 is positive, it opens UP. If the coefficient of x^2 is negative, then the graph opens DOWN.
For example, y =4x^2 -6x +2 opens UP
y=-4x^2 -6x+2 opens DOWN
For additional information on combining parabolas, see my own website. You can do a "Bing" search for my last name "Rapalje". At the top of the search list, look for "Rapalje Homepage". Near the top of my Homepage, look for the link "MATH IN LIVING COLOR." Choose "College Algebra" and look in for Chapter 2 for Section 2.03 Parabolas. I've taught a LOT of methods of graphing parabolas! This is what I consider the easiest way to do it!
R^2
Dr. Robert J. Rapalje, Retired
Seminole Community College
Altamonte Springs Campus
Florida
For the quadratic equation: if a>0 it will open up. if a<0 it will open down.
Let's look at an example:
for a=2, b=2 and c=1
for a=-2, b=2 and c=1
I hope the above steps were helpful.
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