Question

What is the possible discriminant of the graph?

-11
zero
25
73

Answer 1

@mathmate @mathmale any help?

Answer 2

discriminant < 0 means there are no real roots (graph does not touch x-axis)

discriminant = 0 means there is only 1 real root (graph touches only once)

discriminant > 0 means there are 2 real roots (graph touches twice)

Answer 3

As you probably know, the "discrimiant" is the quantity b^2-4ac, which is under the radical in the quadratic formula. Your job here is to approximate the values of a, b and c from the graph and then to calculate the approx. discriminant. As dumbcow has just explained, a positive discriminant implies that there are 2 real roots (which is what your graph shows).

Answer 4

oh wait so the the first and second option cancels out

Answer 5

yes

Answer 6

what do I do after that?

Answer 7

i would approximate the zeroes to be -3 and 1

\[y = a(x+3)(x-1)\]
use point (0,-6) to solve for "a"

distribute to get form y = ax^2+bx+c
calculate discriminate

Answer 8

i am confused

Answer 9

dumbcow's suggestion is a very good one and is probably the easiest approach. I was going to repeat my own suggestion: "As you probably know, the "discrimiant" is the quantity b^2-4ac, which is under the radical in the quadratic formula. Your job here is to approximate the values of a, b and c from the graph and then to calculate the approx. discriminant."

In what way are you confused? What info need you to feel more comfortable?

Answer 10

umm. yes

Answer 11

Yes what?

Answer 12

I don't know how to use:

y=a(x+3)(x−1)

use point (0,-6) to solve for "a"

distribute to get form y = ax^2+bx+c

Answer 13

when i plug in i get a=2 but don't know what i need to do next

Answer 14

dumbcow looked at the graph and found the approximate values of the roots (x-intercepts or zeros). Do you agree that these are approx. -3.2 and +1? In this case it'd be good enough to round those up to -3 and +1.

Why do we care what the roots are? Because, by identifying them, we can reconstruct the polynomial whose roots they are.

Answer 15

can you please show me?

Answer 16

Since dumbcow is absolutely on the right track here, I'm going to let him/her continue.

Answer 17

haha i forgot to mention that if discriminant is a perfect square then the roots must be rational
so we could conclude based on the graph that the only option is 73 since 25 is a perfect square

Answer 18

um.. could you explain the whole process of how the answer is 73 please. I can't seem to understand. i am visual.

Answer 19

@mathmale , i realized by approximating the rounding error on the discriminant is enough to make the answer ambiguous

Answer 20

We have already eliminated two possible answers. That leaves two: 25 and 73. Even with some ambiguity, we should be able to decide which of these two is the closer to what we are observing / calculating, don't you think?

Answer 21

@superhelp101: Please look at the graph again. What is the value of the function when x=0? Of what possible use is this information?

Answer 22

Hint: If y=ax^2 + bx + c, and x=0, y=? c=?