SOLUTION: WHEN y=ax^2+bx+c>0, can u tell me why the graph must be above the x-axis?

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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


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