At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions.

See more answers at brainly.com

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this and **thousands** of other questions

which part of the problem?

The first part for now :)

Hint: Intermediate Value theorem

@freckles do you know any good websites to review the theorem?

could you show me how? please and thank you :)

now let's say we had point A and point B
one point on either side
|dw:1443850712927:dw|

okay

I am kind of confused, how do we know that c=4 is the root that lies in the middle?

because when \(x=0\) (that means it's at the origin) \(y=4\)

ohhh okay

Jhannybean plugged in x = 0 and everything went away basically except for that last term

Exactly

do you understand what part a of the problem is asking? I'm quite confused

if you need a visual way to approach this, draw a blank xy axis
|dw:1443851396111:dw|

at -1 i believe , (-1, 4) ?

now, ask yourself this: is it possible to connect the two points without crossing the x axis?

it is possible

so there is no guarantee we have a root on the interval from x = -3 to x = 0

now IF we had (0,-4) instead, then we shift down the second point
|dw:1443851620081:dw|

|dw:1443851638079:dw|

ohhh okay!

sign change in the y values or function outputs I mean

oh i see now

could you help me on part b?

ok so I think you found that c = 4 right?

do you see how Jhannybean got this?
\[f(-3) = -27a-3b+c=109 \\ f(0) =c=4 \\f(-1)=-a-b+c=15\]

yes :)

wait i don't understand how she got the 109, 4 and15

I think f(-3) should have been 10 and not 109

okay, and how is f(-1)= 15?

it should be
\[f(-3) = -27a-3b+c=10\\ f(0) =c=4 \\f(-1)=-a-b+c=4\]

oh okay, i understand then

oh wait, there's an 11 in there that I missed, let me rethink

Jhannybean has it right, I missed a term

oh ok

Does that make more sense, @heyitslizzy13 ?

yes :)

Great \(\checkmark\)

`that root would be c=4 ` I don't know about that part

so we know c is 4, what about a and b?

Haha, I meant \(x=0\) x_x

ah I gotcha

would it be 109 and 15?

So then you would solve it either by substitution, or using the elimination method :)

can you walk me through either one please? I know what they are but I'm a little lost rn

yes!

Is this making sense, @heyitslizzy13 ?

yes!! :)) is a=-3?

Yes it is :)

okay thanks :)))

can you help me on c also?

thanks!!

thank you both so much!!!! :)))