Rewrite the following functions in intercept form. Find the x−intercepts and the vertex.
1. y = x^2−2x−8
2. y =−x^2+10x−21
3. y = 2x^2+6x+4
4. y = 3(x+5)(x−2)

Question

Rewrite the following functions in intercept form. Find the x−intercepts and the vertex. 
1. y = x^2−2x−8
2. y =−x^2+10x−21 
3. y = 2x^2+6x+4 
4. y = 3(x+5)(x−2)

parthkohli · Answer

hi, nin

parthkohli · Answer

that said, do you have an idea of where to start with this?

anonymous · Answer

this isnt nin.......

anonymous · Answer

im going to kill him now

parthkohli · Answer

yeah, okay.

do you know what "x-intercept" means?

anonymous · Answer

I can help with this one too if you want Parth

anonymous · Answer

.......thanks his gf is stupid....

zzr0ck3r · Answer

I think you mean vertex form?

parthkohli · Answer

yes, back to the question now.

anonymous · Answer

I'm going to assume you know what an x-intercept is, that is where you set your equation to 0

parthkohli · Answer

no, I think the vertex means a point (x,y) where the function is minimum/maximum.

anonymous · Answer

vertex is the (x,y) and is found by using -b/2a to get x coordand plug that back into the equation to find the y coord

zzr0ck3r · Answer

for $f(x) = x^2+bx+c$ the vertex form is $f(x) = (x+\frac{b}{2})^2+c-(\frac{b}{2})^2$

parthkohli · Answer

in the case of quadratic functions, the vertex is given by$$\left(-b/2a, f(-b/2a)\right)$$or, if you notice$$(-b/2a, -D/4a)$$

parthkohli · Answer

$$D = b^2 - 4ac$$

zzr0ck3r · Answer

ok but I dont know what intercept form is, im thinking she was saposed to get it in vertex form, then one can see the vertex....

parthkohli · Answer

x-intercepts = roots of the function

anonymous · Answer

yeah, I'm thinking that should be vertex form which is (x-h)^2+k

zzr0ck3r · Answer

right, what is x intercept form?

parthkohli · Answer

well, I mean the points at which the roots lie.

zzr0ck3r · Answer

lol

zzr0ck3r · Answer

the first line of the question


Rewrite the following functions in intercept form

anonymous · Answer

@msumner, does it ask for intercept form or vertex form?

zzr0ck3r · Answer

maybe intercept form is factored?

anonymous · Answer

it says both

zzr0ck3r · Answer

nah because the last one is factored

zzr0ck3r · Answer

@msumner reread the question, 

does it say put it in vertex form and find the vertex and intercepts

or

does it say put it in intercept form and find the vertex and intercepts?

parthkohli · Answer

I'm going to demonstrate one such question to you.$$y = x^2 + 10x  + 25$$ To get the roots, solve $x^2 + 10x + 25 = 0$.  You will get $x = -5$ as the root.  The point(s) at which the roots fall are the x-intercepts.  Here, the x-intercept is $(-5,0)$.

The vertex is $(-b/2a, f(-b/2a)) \implies (-5,0)$.

anonymous · Answer

To find the x-intercepts, I would first try to factor out the quadratic and if it doesn't factor, use the quadratic formula

anonymous · Answer

This one does factor

parthkohli · Answer

$$y = x^2 + 7x + 12$$Roots:  3, 4
Points/x-intercepts: $(3,0)$ and $(4,0)$.
Vertex: $(-7/2, -1)$

zzr0ck3r · Answer

I will demonstrate a similar  equation in vertex form, (just in case) 

$y = x^2+10x+12 = (x+5)^2+12-25 = (x+5)^2-13$

anonymous · Answer

Really good examples here, @msumner take notes :)

parthkohli · Answer

The vertex form in general is$$ax^2 + bx + c = a\left(x + \dfrac{-b}{2a}\right)^2 + \dfrac{4ac - b^2}{4a}$$

anonymous · Answer

That is standard form I thought

parthkohli · Answer

Yes, that's the standard form for the vertex form.

anonymous · Answer

vertex form that I know is (x-h)^2 + k

nincompoop · Answer

I didn't know parabolas have intercept form :D

zzr0ck3r · Answer

they are the same thing,... parth just showed how to get there from ax^2+bx+c

zzr0ck3r · Answer

there is no such form as far as I know....

zzr0ck3r · Answer

on any function

parthkohli · Answer

I mean there is$$\left(\dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}\right)$$

parthkohli · Answer

and the y-coordinate is zero.

anonymous · Answer

The intercept form of a quadratic equation is as follows:

 y=a(x−p)(x−q)

nincompoop · Answer

there is the standard form and the general (vertex) form that I know of

anonymous · Answer

I just found that when I was looking it up

parthkohli · Answer

so... the factored form.

zzr0ck3r · Answer

I almost guarantee the OP needed to put them in vertex form and then use that form to see the vertex clearly...

anonymous · Answer

that is what it is called

zzr0ck3r · Answer

vertex form, completing the square, the quadratic formula are all the same thing...

parthkohli · Answer

Well, anyway, there's the general form.  You may not even feel the need to complete the square.  They're the same processes though, so feel free.

anonymous · Answer

I think it is just faster in general to use the quadratic formula unless I can see right away that it can be factored

nincompoop · Answer

what is this?  y=a(x−p)(x−q)
what is the q and what is the p? and what is the x in there?

nincompoop · Answer

we are throwing bunch of letters LAUGHING OUT LOUD

parthkohli · Answer

Of course, but the quadratic formula ain't no help with your vertex.

anonymous · Answer

p and q are the x-intercepts (also zeros, solutions, roots)
a is the vertical stretching factor

anonymous · Answer

there is the context to the intercept form (factored form)

zzr0ck3r · Answer

if you get fast at completing the square you can solve them faster than you can write down the quadratic formula

zzr0ck3r · Answer

jt the last one is in factored form

nincompoop · Answer

always convert from standard to vertex by completing the square if the equation isn't already a completed square

zzr0ck3r · Answer

so I ruled that out

skullpatrol · Answer

Any questions @msumner ?

zzr0ck3r · Answer

all in all I feel bad for the person that asked this question

zzr0ck3r · Answer

lol @skullpatrol

nincompoop · Answer

LAUGHING OUT LOUD

anonymous · Answer

yeah, she got a lot of information just now
I hope we don't overwhelm her

parthkohli · Answer

She started with four questions.

She must have double of them now.

nincompoop · Answer

I am glad I am only in pre-algebra

zzr0ck3r · Answer

she started writing and just said f**k it

anonymous · Answer

I am in pre-calculus

zzr0ck3r · Answer

im in algebra

zzr0ck3r · Answer

544:)

parthkohli · Answer

I'm 8 and what is this

anonymous · Answer

im good lol

anonymous · Answer

wait, if you are in algebra and pre-algebra, how do you know algebra 2 concepts?

zzr0ck3r · Answer

im in abstract algebra as a graduate student:)

anonymous · Answer

thanks guys hahaha..... nin is just confusing you .....

anonymous · Answer

ah, that explains it :)
anyway, hope we helped you out @msumner and sorry for the long explanations

parthkohli · Answer

nin, why are you referring to yourself in third person?

zzr0ck3r · Answer

lol

anonymous · Answer

its fine i got a laugh out of it :)..... im not nin smarty

anonymous · Answer

http://strawpoll.me/1831262/r

zzr0ck3r · Answer

adding a y to the end of words makes you sound like a girl

zzr0ck3r · Answer

its girly

anonymous · Answer

that is awesome @iambatman, I am adding that to my bookmarks

anonymous · Answer

Spelt the name wrong, no biggie, just being a nincompoop today.

anonymous · Answer

im a girl named mickie

anonymous · Answer

you don't have to tell us your real name

parthkohli · Answer

*sigh* nin, is that the best name you could come up with?

anonymous · Answer

who said that was my real name

zzr0ck3r · Answer

thats a lie, no parent would name a girl mikey

anonymous · Answer

Unless they're fan of rats

anonymous · Answer

lol its a nickname

parthkohli · Answer

of course it's not your real name

your real name is what nin's real name is

you're nin

zzr0ck3r · Answer

was that a goonies joke?

anonymous · Answer

I will let you guys figure out this mystery and I will get back to my hw

anonymous · Answer

lol