Another variables question a little harder this time.

[davie08]

Homework Statement

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

Homework Equations

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.

 

[Mark44]

Homework Statement

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

Homework Equations

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.

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

Solve the resulting quadratic equation.

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

 

[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.

 

[Mark44]

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.

 

[davie08]

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

 

[SteveL27]

Homework Statement

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

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.

 

[davie08]

thanks steve you 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.