# Another variables question a little harder this time.

1. Aug 5, 2011

### davie08

1. The problem statement, all variables and given/known data
Which of the following points is a point of intersection of the graphs
f(x)=x^2+35 and g(x)=12x?

multiple choice

-(0,35)

-(9,35)

-(1,12)

-(5,60)

-(9,60)

- none of the above

2. Relevant equations

3. The attempt at a solution

I haven't done any math for 3 years so bear with me I'm not even sure how to begin answering this question, and don't worry I don't even care about the actual answer I just want to find out how to get it.

2. Aug 5, 2011

### Staff: Mentor

Set the two functions equal.
x2 + 35 = 12x

There are two points of intersection, one of which is listed.

3. Aug 5, 2011

### davie08

okay so you would substitute 5 for x and end up with 60. So would that make the answer (5,60). If this is the answer how does that work where the number your substituting is the first number of the intersection.

4. Aug 5, 2011

### Staff: Mentor

When you set x2 + 35 = 12x, you are setting the y values of the two functions equal, and solving for x. At any point of intersection, there is a point (x, y) that is on both graphs.

Solving the quadratic, you get x = 5 or x = 7. f(5) = g(5) = 60, the y value at the intersection point (5, 60). f(7) = g(7) = 84, so the other point is (7, 84), which isn't listed.

5. Aug 5, 2011

### davie08

thanks again luckily im taking a math readiness course in a couple weeks I only know a 1/4 of these questions.

6. Aug 5, 2011

### SteveL27

The other responders gave you the general method, but in this particular case we can just eyeball it and get the answer.

The question is asking, which of those points can be a point on the graph of BOTH of those functions. g(x) = 12x is particularly simple to work with, and you can see that if you plug in 0, you get 0; if you plug in 9, you get 108, and so forth. Mentally testing out each of the points, we see that only (1,12) and (5,60) are on the graph of g(x) = 12x. So those two are the only possibilities.

Now looking at f(x)=x^2+35, if we plug in 1 we get 36, so (1,12) is impossible. And if we plug in 5, we get 5*5 + 35 = 60. Voila!

The moral of the story is that it's important to know the general method: set the two functions equal and solve the resulting quadratic. But it's equally important -- really, MORE important -- to always take a moment to stop and think about the meaning of the question, and see if you can get a sense of what's going on without putting pencil to paper. This particular problem happens to be solvable by just looking at it and thinking about what the question means.

Last edited: Aug 5, 2011
7. Aug 5, 2011

### davie08

thanks steve ya I realize that because it makes a question so much easier when you truly understand what it means verse just memorizing the methods to find that answer.