|
Question 969032: WHEN y=ax^2+bx+c>0, can u tell me why the graph must be above the x-axis?
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website! WHEN y=ax^2+bx+c>0, can u tell me why the graph must be above the x-axis?
Look at this set of axes:
All the numbers marked on the y-axis above the x-axis are all positive.
All the numbers marked on the y-axis below the x-axis are all negative.
The positive numbers are the numbers greater than 0.
The negative numbers are the numbers less than 0.
Your inequality states:
y = ax^2+bx+c > 0
The important thing is that it says that y > 0,
or y is greater than 0, which means that y is positive.
So that can only be where the y-axis has positive numbers
marked on it, which is above the x-axis.
Edwin
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! all the graph doesn't have to be above the x-axis.
they are looking for the parts of the graph that are above the x-axis.
the x-axis is when y = 0.
you solve for y = ax^2 + bx + c > 0 by setting y = ax^2 + bx + c = 0, and then finding the area of the graph that are above the x-axis.
here's an equation.
y = x^2 + x - 6.
if they ask you to find wyhen x^2 + x - 6 is greater than 0, you would first find when x^2 + x - 6 is equal to 0 and then look for the areas of the graph that are above the x-axis.
in this problem, you would do the following.
you would find the roots.
they would be at x = 2 and x = -3.
you would then determine the regions of the graph.
they would be x < -3, -3 < x < 2, x > 2.
you would then test each region to see if the value of y is positive or negative.
your eqution is: y = x^2 + x - 6.
when x = -5, y is equal to 14.
when x is equal to 0, y is equal to -6
when x is 5, y is equal to 24.
the graph is positive when x < - 3.
the graph is negative when -3 < x < 2.
the graph is positive when x > 2.
that would be your solution.
here's what that graph looks like:
you can see from the graph that x^2 + x - 6 > 0 in the intervals we just calculated.
here's a reference on polynomial inequalities you might find useful.
http://home.windstream.net/okrebs/page32.html
here's another one.
http://www.regentsprep.org/regents/math/algtrig/ate6/quadinequal.htm
|
|
|
| |
