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Question: A parabola has intercepts of x = -2, x = 3, and y = -4.
Answer these
a. Write the intercept form of the parabola.
b. State the direction of the parabola. Explain.
c. Write in ax2 + bx + c form.
d. What is the axis of symmetry?
e. What is the vertex?
f. Graph the parabola. Label axis, vertex, and intercepts.

- anonymous

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- anonymous

@Nnesha please help?

- Nnesha

what is the intercept form ?
ax^2+bx+c = standard form
y=a(x-h)^2+k vertex form

- anonymous

thank you @Nnesha :D

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## More answers

- Nnesha

x=-2 , x=3
set it equal to zero

- anonymous

okay... then do I plug in something?

- Nnesha

then you would apply foil method to get the standard form

- anonymous

foil method? o.o//

- Nnesha

(a+b)(c+d) multiply ? FOIL familiar with it ?

- anonymous

-2^2 +3+-4=

- anonymous

??? cross multiply, sorry I don't really remember...

- anonymous

...

- anonymous

y=(x^2+x^3)^4 ???

- Nnesha

this is the intercept form of parabola \[\huge\rm y=a(x-p)(x-q)\]
where p and q are the x-intercepts
y= y-intercept

- Nnesha

a)^^

- Nnesha

given x-intercepts are -2 and 3
so substitute p and q for -2 and 3

- Nnesha

\[\huge\rm y=a(x-(-2))(x-3)\]
y intercept is (0 , -4) { y-intercept is a point where graph of the equation intersect y-axis when x=0 )
so substitute y for -4 and 0 for x
solve for a

- anonymous

I never really learned this, so don't be mad... Anyways okay

- Nnesha

i've never heard abt intercept form
this is first time i'm doing this

- Nnesha

feel free to ask question if you don't get anything :)

- Nnesha

http://www.virtualnerd.com/algebra-2/quadratics/transforming-functions/intercept-form/intercept-form-from-graph
i watched this video
watch this maybe you will understand
like i said today is the first time i'm solving intercept form
already familiar with vertex , standard form but not the intercept :D

- anonymous

a= - y/2x(x-3)

- anonymous

a=−y2x(x−3)

- anonymous

okay :/

- anonymous

@Robert136 please help?

- Nnesha

replace y with -4

- Nnesha

read the statement of the original question

- anonymous

a=-4/2x(x-3)

- Nnesha

\[-4=a(x-(-2))(x-3)\]
when y =-4 x would be 0
bec when line intersect at y-axis x=0
so replace x with 0

- Nnesha

\[\huge\rm -4=a(\color{reD}{0}-(-2))(\color{reD}{0}-3)\]
like this now solve for a

- anonymous

a=2/3

- Nnesha

yes right so intercept for would be ?
\[\huge\rm y=a(x-p)(x-q)\]
replace a with 2/3
p =-2
q=-3

- anonymous

y= 1/2 (x --2) (x--3)?

- Nnesha

a =2/3 not 1/2

- anonymous

opps xD i don't know where that came from xD

- Nnesha

\[\huge\rm y=\frac{ 2 }{ 3 }(x\color{reD}{-(-2)})(x-3)\]
distribute -(-2)

- anonymous

y=2/3(x--2)(x--3)

- Nnesha

hmm q isn't -3

- Nnesha

\[\huge\rm y=\frac{ 2 }{ 3 }(x\color{reD}{-(-2)})(x-(+3))\]
distribute -(-2)

- Nnesha

-1 times -2 = ?
- times +3 = ?

- anonymous

-2?
3

- Nnesha

after that you wll with part a

- Nnesha

negative times negative = positive

- Nnesha

so -1 times -2 = ?

- anonymous

2

- Nnesha

yes so
-1 times 3 = ?

- anonymous

-3?

- Nnesha

right

- anonymous

okay xD

- anonymous

2, -3

- Nnesha

\[\huge\rm y=\frac{ 2 }{ 3 }(x+2))(x-3)\]

- anonymous

y=2/3(x+2)(x-3)

- anonymous

lol

- Nnesha

yep!

- anonymous

xD ♥

- Nnesha

now multiply 2/3(x+2)(x-3)
and i've to go now sorry
its urgent :(

- Nnesha

for part b) if a is positive then you will get`u` shape
and if a is negative then you will hve `n` shape

- Nnesha

cya

- anonymous

sorry I had to go the restroom...

- Nnesha

are you there ?

- Nnesha

tag me when u're ready okay :)

- anonymous

hey

- anonymous

still here sups, aha

- Nnesha

okay great ready !?

- Nnesha

`Write in ax2 + bx + c form. `
multiply 2/2(x-3)(x+2)

- anonymous

okay hold up

- anonymous

x^2-x-6?

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @Nnesha
`Write in ax2 + bx + c form. `
multiply 2/2(x-3)(x+2)
\(\color{blue}{\text{End of Quote}}\)
2/3**

- Nnesha

(x+2)(x-3)=x^2-x-6 now multiply it by 2/3

- anonymous

okay

- Nnesha

let me know what u get

- anonymous

I get nothing :/

- Nnesha

what do you mean ?

- anonymous

I get 0

- anonymous

also sorry I had to leave the computer
:/

- Nnesha

how did you get 0 ??
2/3(x-3)(x+2) ??

- anonymous

multiplied....

- anonymous

2x^2/3 - 2x/3 -4???

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