Question

What is the possible discriminant of the graph?

a parabola opening up with vertex near negative 1.2 comma negative 9.1. a y intercept of negative 6

-11
zero
25
73

Answer 1

@satellite73 could you please help meh on this problem?

Answer 2

@robtobey please i need your help?

Answer 3

@satellite73 can you help

Answer 4

@radar can you please help me

Answer 5

@radar @satellite73 @robtobey my only hopes i have. I really need your help

Answer 6

@aaronq please i need youuuu

Answer 7

@Luigi0210 @radar @radar radar i need u man... just this question is confusing me

Answer 8

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I will love u if you help me <3

Answer 9

Is this the problem?

Answer 10

yep!

Answer 11

Lets see what aum has to say.

Answer 12

In \(\Large y = ax^2 + bx + c\),

the y-intercept is c,
the sum of the roots = -b/a
the product of the roots = c/a

You can read the roots and the y-intercept off of the graph.

Answer 13

Solve for a, b and c.
Discriminant = \(b^2 - 4ac\)

Answer 14

could u help me with finding the discriminant

Answer 15

What is the y-intercept from the graph?
What are the roots (or x-intercepts) from the graph?

Answer 16

umm..

Answer 17

Actually in the statement of the problem they give you the y-intercept.

Answer 18

@aum The problem states the y intercept is -6, does that make c=-6

Answer 19

i think so. yes

Answer 20

Yes, c = -6
If we put x = 0 in y = ax^2 + bx + c
we get y = c

Answer 21

Thanks, is that enough for you to solve this problem @superhelp101?

Answer 22

um I really am stuck with what to do next

Answer 23

Read the x-coordinates of where the graph crosses the x-axis. Those are the roots.

Answer 24

sorry I am dumb.

Answer 25

ok I understand to that point

Answer 26

What are the x-coordinates of where the graph crosses the x-axis?

Answer 27

(-3.306, 0) and (.806, 0)

Answer 28

Look at the left most root where y=0, it states x= my eyes are bad, but it looks like a negative 3.

Answer 29

Oh it is 3.306 (all I could see was the -3.

Answer 30

yep

Answer 31

Yes, the roots are -3.306 and 0.806.
Multiply the roots and equate it to c/a
We already know c = -6
So you can solve for a.

Answer 32

wait I think i got 73 as my answer. Am i right?

Answer 33

Looks pretty straight forward, what do you get for a @superhelp101 ?

Answer 34

Lets see what i get (-3.306)(0.806) =-6/a
-2.664636 =-6/a
a=-6/-2.664636
a=2.251714681
That was not 73, @aum am I off the rail here?

Answer 35

I am getting a = 2.252 too (up to 3 decimals as their x-intercepts are up to 3 decimals).
c = -6
sum of roots = -3.306 + 0.806 = -2.5 = -b/a
b = 2.5 * a = 2.5 * 2.252 = 5.63

b^2 - 4ac = (5.63)^2 - 4(2.252)(-6) = 85.745

Answer 36

The above values of a.b and c are correct because the equation:
2.252x^2 + 5.63x - 6 = 0
gives the same roots as given in the problem and has the same y-intercept.

https://www.wolframalpha.com/input/?i=2.252x^2+%2B+5.63x+-+6+%3D+0

Answer 37

my answer choices don't have 85
only has
-11
zero
25
73

Answer 38

The discriminant is a positive rational number 85.745 which is not the square of an integer that should mean the roots are irrational........right.

Answer 39

"What is the possible discriminant" ..... "vertex near"
seems to suggest they want an estimate or an approximate value.
So I'd probably go with 73.

Answer 40

@superhelp101 you must select the best answer, I too would go with the 73, definitely not 0 or -11.

Answer 41

ok that's what i would go with too. i will tell you if that was right or wrong, just a sec for it to grade

Answer 42

I am waiting with bated breath....

Answer 43

IT WAS RIGHT! I LOVE U GUYS

Answer 44

Wheeeeewwwwww!!

Answer 45

I LOVE YOU GUYS! I understand

Answer 46

Give aum the medal.

Answer 47

i did, but I was going to give both of you guys. Both helped me

Answer 48

I could only give one

Answer 49

Thanks for staying with us @aum

Answer 50

radar's earlier reply made me realize we could have saved a whole lot of these calculations and quickly picked 73 as the "possible" discriminant because:
We know the roots are REAL and that the roots are NOT INTEGERS.
Therefore, the discriminant cannot be negative and the discriminant cannot be a perfect square such as 25 or a zero because both of those will give rational roots.

Answer 51

Slap. hand hitting forehead. lol

Answer 52

lol

Answer 53

Lol

Answer 54

it's ok, we all learned something new today, right?

Answer 55

I did, I am saying 73, which in ham radio means best regards. Good day and good luck.

Answer 56

thank you!

Answer 57

I meant to say: From the graph we know the roots are REAL and the roots are possibly IRRATIONAL rounded to three decimal places. Real roots rule out negative discriminant.
Two DIFFERENT roots implies the discriminant is not zero. Two irrational roots rule out
a perfect square discriminant which leaves just 73 as the only possible answer choice.