Question

Identify the graph of a quadratic equation with two different rational solutions.

Answer 1

a quadratic equation has 2 solutions, which may be identical. a real solution occurs where the curve crosses the x-axis (y=0). a rational solution is one where the solution can be expressed as a quotient of two integers. given that information, which is your choice for the correct answer?

Answer 2

crosses or touches the x-axis, to be clear...

Answer 3

Well its not D then :3 right?

Answer 4

D doesn't make contact with the x-axis, so it only has complex roots and can be eliminated from consideration here. So far, so good...

Answer 5

Its not C either :3

Answer 6

right? XD

Answer 7

@whpalmer4 ? :(

Answer 8

is it B? @whpalmer4

Answer 9

I need help with this >.> since this question belongs to one of my pretests, and pretests are took when you don't study anything in the lesson to test you, I really havent studied this yet T_T

Answer 10

can you tell me why it isn't A or C?

Answer 11

A is continues, and C has only one point plotted on the graph :3 so the answer is B? :O

Answer 12

"A is continues"? what does that mean? oh do you mean the decimal representation continues?

Answer 13

yes ^-^

Answer 14

C has a whole bunch of points plotted on the graph, but only one on the x-axis :-)

Answer 15

@whpalmer4 ahhhh :O and I was right about a right? that its continues (the decimal point thing) XD

Answer 16

so, yes, B is the answer...

Answer 17

@whpalmer4 thank you so much ^-^

Answer 18

we don't actually KNOW that A is incorrect from the decimals that they showed, but it looks like it is, and we can see that B is a completely correct choice.

Answer 19

@whpalmer4 ahhh I see :D thanks for the help! :)

Answer 20

it looks like A might have solutions of \[-1\pm\sqrt{2}\] as \[\sqrt{2} \approx 1.414\]

Answer 21

@whpalmer4 ahhhh :O so b is the correct answer :) right? XD

Answer 22

B is an unambiguously correct answer.

Answer 23

@whpalmer4 XD thanks for ur help :D

Answer 24

just because the decimal representation goes on forever doesn't make a number irrational. for example, 3/7 = 0.428571428571 etc. but it is definitely a rational number!

Answer 25

@whpalmer4 I see :D lol thanks to u not only did I get help on the question and an answer, but I actually understand this now ^-^ THANKS! :D

Answer 26

that's always the goal, glad I could help :-)

Answer 27

As a little bonus :-)

Here's a parabola I found which has almost identical solutions, identical vertex, and the solutions are both rational and repeating in their decimal representation. B is still a better answer, but from the graph, you can't rule out the possibility that A was the polynomial I found, which would also be a correct answer.