Calc Summer Assignment

[CrystalTennis]

Hello I am trying to complete my summer assignment and I am stuck! How do I find the points of intersection for the following?
a) f(x)=x^2 -4 and g(x)=3x +20
b) f(x)=x^2 +6 and g(x)= 3x^2 +x
c) f(x)=x^3 -1 and g(x)= 2x^2 -1
I have tried to start but I am utterly stumpted!!! Please Help!

 

[mmm4444bot]

How do I find the points of intersection for the following?

a) f(x)=x^2 -4 and g(x)=3x +20

Do you realize that f(x) and g(x) are symbols for y?

At the intersection point(s), the value of y will be the same for both the parabola (function f) and the line (function g).

This means that f(x) = g(x) at the intersection point(s).

Hence, you need to find the value(s) of x where f(x) equals g(x).

Does this information give you any ideas about writing an equation to solve?

Next time, please include what you've already tried (even if you think that it's wrong), so that we have something better to go on.

Cheers :cool:

 

[CrystalTennis]

Sorry!

okay I think I was supposed to get the answer by work... so I got to the point 0=x^2 -3x -24 then i used the quadratic and I got 6.6235 and -3.6235 so I plugged them into the g(x) equation. Then I got (6.62, 39.87) and (-3.62, 9.13) as points... did I do it correctly. It took me 5 hours to get this far.

 

[mmm4444bot]

I got

0 = x^2 - 3x - 24

i used the quadratic [formula] and I got 6.6235 and -3.6235

I plugged them into the g(x) equation

I got (6.62, 39.87) and (-3.62, 9.13) as [the intersection] points

did I do it correctly. It took me 5 hours to get this far.

Yes, those are the two intersection points, and you did it correctly.

You could have verified your result, by evaluating f(6.6235) and f(-3.6235) and comparing to the values of g(6.6235) and g(-3.6235) that you already calculated; both f and g must have the same coordinates at those points because that's what intersection means.

With practice, maybe (b) and (c) will only take 20 minutes. Cheers :cool: