Question

algebra 2 question?

Answer 1

How are you, Mr. Plohrr?
Might help to sketch some possibilities where a second order equation and a first order equation are involved.
A second order equation might look like this: y=3x^2 -5x +1, whereas a first-order equation like: y=-2x + 3.
With that in mind, what do you think the question is asking us?

Answer 2

"Mr. Plohrr" is, of course, an effort to be witty; I'm not that formal. :)

Answer 3

give them a situation where one is right and one is wrong, specific equations

Answer 4

Are you good at sketching simple graphs quickly?
If so, graph y=x^2 and y=-1 on the same set of coordinate axes.
Do the 2 graphs intersect?

Answer 5

no and they never will

Answer 6

Right. So this is a case of "no solution."
Now suppose you cross out your graph of y=-1 and replace it with a graph of y=0. What could you conclude, based upon your graph of the parabola and the line y=0?

Answer 7

they intersect at one point

Answer 8

Cool.
Now suppose you cross out your graph of y=0 and replace it with a graph of y=2.
Conclusion(s)?

Answer 9

intersection at 2 pts

Answer 10

So now we've explored three different possibilities.

Suppose your 2nd order eq'n is y=x^2, as before, and your str. line (first order equation ) is y=2 (as before). Is it possible for you to replace the y in your y=x^2 with y=2? If so, can the resulting eq'n be solved for x?

Answer 11

yes?

Answer 12

Look: y = x^2. But the other equation is y=2.

Substituting, y = 2 = x^2.

can that be solved for x?

Answer 13

hmm yes it can

Answer 14

And how many solutions will there be?
I like to teach by asking questions wherever possible. I don't mean to stretch this out forever, but do think it will benefit you in the long run to experiment with guidance, as you and I have been doing.

Answer 15

one solution

Answer 16

But if x^2 = 2, and we take the sqrt of both sides, we end up with x = plus or minus Sqrt(2). Can you agree with that? Every 2nd order equation has 2 roots.

Answer 17

oh yeah so 2 solutions

Answer 18

So, in summary, Peter, it's possible that the solution of a system involving one quadratic (2nd order) equation and one linear (first order) equation can include two points; there are 2 solutions.

But if we abandon y=2 and revert to y=0, we'd have how many solutions?

Answer 19

1

Answer 20

Suppose y=0 and we substitute that into y=x^2. What would the resulting equation look like, and would it have a sol'n? If so, what would the sol'n be?

Answer 21

Glad you caught that. The answer is 1 (not 0).

OK so far?

Answer 22

yep

Answer 23

Everything OK with you? I sense your attention is partially elsewhere this afternoon.

Now suppose y=-2. How many solutions will this system have?
that is, the system y=-2 and y=x^2

Answer 24

no im just disappointed bc i lost in the finals of my tournament, but i have to get this done

Answer 25

0 solutions

Answer 26

I'm extremely sorry to hear that. Hope it's not the end of the season, and that you and your team will have additional chances to come out on top.

Answer 27

Right. 0 solutions.

so now y ou've seen it all.

Depending on whether or not the 2nd order equation's graph and the graph of the line intersect, this system may have 0, 1 or 2 solutions. That's basically all you need to answer this question. Are you OK with this? Or have3 more questions about this probelm?

Answer 28

thanks :)

Answer 29

i do have more but not on this topic

Answer 30

You're welcome! Are you up to working on problems from some other topic?

Answer 31

of course :)

Answer 32

Good! Mind posting a new problem separately?