+0  
 
0
90
6
avatar+121 

Suppose f(x)= (x-8)(x+5)

For which values of x is the function f(x) positive? Enter your answer using inequalities.

 

I believe -5>x>8 is correct? apparently not?

vest4R  Feb 28, 2017

Best Answer 

 #4
avatar
+5

The way to solve these   -always-     is to sketch the graph of the quadratic.I can't use the graphics on this site,but I'll try to explain.

This function is a parabola which touches the x axis at the points (-5,0)  and (8,0). You should sketch it to be clear. When x is less than   -5,f(x)   is positive    and when  x is greater than 8 f(x) is positive.  So you have the UNION of two inequalities, not what you have written above. Answer is ( can't write this in symbols because of software)

 

 x  is les than  (-5)      U       x is greater than 8 

Guest Feb 28, 2017
Sort: 

6+0 Answers

 #1
avatar+89777 
0

Hi vest4R,

 

"I believe -5>x>8 is correct? apparently not?"

 

this says

 

-5 is greater than x and x is greater than 8 ...

 

if -5 is greater than x then x must be less than -5

if x is less then -5 how can it be greater than 8  ???

 

See my problem?

Melody  Feb 28, 2017
 #2
avatar+89777 
0

Are you gong to respond to me vest4R ??

Melody  Feb 28, 2017
 #3
avatar+121 
+5

thank you melody, I see what you mean.

 

I'm just trying to work out how to write it now.

vest4R  Feb 28, 2017
 #4
avatar
+5
Best Answer

The way to solve these   -always-     is to sketch the graph of the quadratic.I can't use the graphics on this site,but I'll try to explain.

This function is a parabola which touches the x axis at the points (-5,0)  and (8,0). You should sketch it to be clear. When x is less than   -5,f(x)   is positive    and when  x is greater than 8 f(x) is positive.  So you have the UNION of two inequalities, not what you have written above. Answer is ( can't write this in symbols because of software)

 

 x  is les than  (-5)      U       x is greater than 8 

Guest Feb 28, 2017
 #5
avatar+89777 
0

Thge easiest way to do a question like this is to think about the graph

f(x)= (x-8)(x+5)

 

This is a concave up parabola.  The roots are at  x=8  and  x=-5

 

Since it is concave up it is the bit inbetween these points that falls BELOW the x axis.  and that is where f(x)<0

 

The ends are where f(x)>0

 

so      x<-5    and   x>8

 

here is the graph.

 

Melody  Feb 28, 2017
 #6
avatar+121 
+5

thank you melody. I really appreciate it. The help you give out on this website is top class.

 

It turns out I haven't learned about union's just yet nor did I know they existed.

 Thank you for putting me on the correct path.

vest4R  Feb 28, 2017

7 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details