how do I do this??

[silk flame]

A quadratic equation has the form
[ y = ax^2+bx+c = a(x-d)^2+e ]
where $V(d,e)$ denotes the vertex.

[halcyon bay]

bacc

[fair knot]

Yeah

How do I find the a

[silk flame]

plug in the points

y = ax^2 you know (20,-150)

solve for a

[fair knot]

Are those both X coordinates? Or is -150 y @silk flame

[silk flame]

what

no

(x,y)

a point always has one value of 1 dimension

-150 = a(20)^2 solve for a

[fair knot]

So a = 400?

[silk flame]

how

[fair knot]

20^2

[silk flame]

what

-150 = a(20)^2 is your equation

not a = (20)^2

[fair knot]

I don’t really get it, could you give me a example with a different equation or something

[silk flame]

2x = 6

what is x

surely not 2

[fair knot]

Its 3

[silk flame]

what do you need to do

ye how

[fair knot]

Cause 2 times 3 equals 6

[silk flame]

ok

-150 = 400a

what is a

it cannot be 400 you would get 160000

divide by 400

a = -150/400

,calc -150/400

[halcyon bay]

Result:

-0.375

[silk flame]

that should be -3/8

if you divide by 50

so then a = -3/8

y = (-3/8)x^2 done

[fair knot]

Did you just simplify it to -3/8? Or how did you get that?

Oh wait nevermind

[silk flame]

common divisor 50

[fair knot]

Yeah, I see that now

So would the answer for the question be

F(x) = -3/8 (x + 0) + 0??

[silk flame]

bro the square

and you dont need the zeros

simplify it

[fair knot]

Oh Ok

So its just
f(x) = -3/8x^2?

@silk flame is question b)
y = 27/2x^2 ??

[silk flame]

no

vertex is (8,0)

[fair knot]

Yeah

[halcyon bay]

bacc

[silk flame]

vertex formula

now find a

bro

[fair knot]

So do I put 2 where the X is?

[silk flame]

yes

and for y=

[fair knot]

Ok

[silk flame]

y =?

[fair knot]

54

[silk flame]

good

now solve

i am nice

[fair knot]

Ok, one second

[halcyon bay]

bacc

[fair knot]

Im at 54 = a(-36)
What do I do from here?

[silk flame]

wrong

(-6)² = 36

a square is never negative

54 = 36a

[fair knot]

Oh

Ok

[silk flame]

now isolate a

[fair knot]

So divide both sides by 36?

[silk flame]

yes

a = 54/36

reduce the fraction

I think 6 is common divisor

a = 9/6

a = 3/2

[fair knot]

Ok

So the answer is
f(x) 3/2 (x+8)^2

[silk flame]

-8

f(x) = 1.5(x-8)^2

[fair knot]

Wait why is it -8?

[silk flame]

the vertex is at (8,0)

d = 8

e = 0

y = a(x-d)+e

[fair knot]

Ohh

How do I do C?
Im stuck at
12 = 16a + b(-4) + 60

[silk flame]

minimum value at x = -4 implies a vertex

(-4,12)

y intercept 60 do c = 60

[halcyon bay]

bacc

[silk flame]

use now the fact that (0,60) is also a point on the parabola

[fair knot]

Ok

So put 60 into the Y and 0 into the X right?

[silk flame]

ye

[fair knot]

K

I got a = 15/2

[silk flame]

,calc (60-12)/4^2

[halcyon bay]

Result:

3

[silk flame]

hmm

[halcyon bay]

bacc

bacc

[silk flame]

both divisible by 16

3=a

[fair knot]

Darn it! I forgot to square 4

[fair knot]

How did 60 become 48?

[silk flame]

subtract 12

[fair knot]

Ok, I get it now

[silk flame]

do you?

[fair knot]

Yeah, its starting to make sense

[silk flame]

prove it

do d) on your own

[fair knot]

Alright

[fair knot]

Well I tried, how do you find the X vertex?

[silk flame]

You can derive the vertex' x-coordinates based on the x-intercepts

it is always the middle distance between your x-intercepts

what is the middle between 2 and 7

[fair knot]

So 4.5

[silk flame]

no

(2+7)/2

ye

4.5

so your vertext is V(4.5, 12) maximum

[halcyon bay]

bacc

[silk flame]

Now you can either plug in (2,0) or (7,0)

to get a

[fair knot]

Ok! Let me try it from here

a = 4

Right?

[silk flame]

let me see

,calc -12/(7-4.5)^2

[halcyon bay]

Result:

-1.92

[fair knot]

?

a = -1.9?

[silk flame]

-1.92

,w plot y = -1.92(x-4.5)^2+12

roots are 2 and 7

vrtex at (4.5, 12)

[fair knot]

I thought it was (4.5, 25)

[silk flame]

oh shit

why didnt you say that

[silk flame]

...

start again

let me see

[ y = a(x-4.5)^2+25]

[halcyon bay]

bacc

[silk flame]

you said 4 previously that cannot be either because it has to be negative since the vertex is maximum

,calc -25/(2-4.5)^2

[halcyon bay]

Result:

-4

[silk flame]

-4

ye

[fair knot]

Ok, I was close

[silk flame]

[y=-4(x-4.5)^2+25]

[halcyon bay]

bacc

[silk flame]

,w plot y=-4(x-4.5)^2+25

[halcyon bay]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by adoniszgks

[fair knot]

Im not supposed to have decimals in my answers though, so how would I write 4.5?

Would it be 9/2?

[silk flame]

yes!

[fair knot]

Hmm Ok Ok

Well I dont have any more questions that are like this, and section 5 I can do but I might need help later for section 6, so I could be back later

[silk flame]

you could

[fair knot]

Yeah, but I got a test tomorrow and I would just like to do all the different kinds of questions for it

Cause theres a few I dont understand

[silk flame]

ok

[fair knot]

@silk flame
I got f(x) = -90 (x - 0)^2 + 56

Is this correct??

??

If you dont mind helping me again @silk flame

[silk flame]

It has a depth right

[fair knot]

Right

[silk flame]

sounds like a minimum

[fair knot]

Yep

[silk flame]

so it should be 90 not -90

facing upwards

[silk flame]

you can see it on the picture

[fair knot]

Ohh Ok, so is it right besides the -90

[silk flame]

You know it has a maximal width of 180

[fair knot]

Yeah

[silk flame]

Say the vertex is (0,-56)

,, y = ax^2-56

[halcyon bay]

bacc

[silk flame]

So from -56 to 0

at 0 we wanna have a maximal width of 180

so actually we have roots at -90 and 90

[fair knot]

Ohh

And roots are X - intercepts right?

[silk flame]

yes

,, 0 = 90^2a-56 \Leftrightarrow 56 = 90^2a

[halcyon bay]

bacc

[silk flame]

,calc 90^2

[halcyon bay]

Result:

8100

[silk flame]

,, a = \frac{56}{8100} = \frac{14}{2025}

,, y = \frac{1}{150}x^2-56

[halcyon bay]

bacc

bacc

[fair knot]

so a = 14/2025

[silk flame]

ye

[fair knot]

So the answer would be

f(x) = 14/2025 (x - 0)^2 + 56

Or

f(x) = 14/2025^2 + 56

[silk flame]

x^2

you forgot the x^2

[fair knot]

Wait is this a?

[silk flame]

a is the 14/2025

[fair knot]

Ok
How’d you get the
1/150?

Was it from

8100/56?

Yeah you dis

[silk flame]

yea this wrong

[halcyon bay]

bacc

[fair knot]

So you now have
-56 = 14/2025x^2

Now what?

[silk flame]

what are you doing

[fair knot]

Im just kinda lost now, where are we at?

[silk flame]

finished

[silk flame]

that's the function equation

[fair knot]

Ohh

Your right

My bad

When did the 56 become -

[silk flame]

We started with the vertex V(0,-56)

it doesnt matter actually here

but the thing is it's that way easier

if it were +56

then you would have to do more tedious calculations

then you would have instead (56+56, -90) and (56+56,90)

[fair knot]

Hmm alright

Im gunna try section 7 before I ask for help

@silk flame for the first one I got

f(x) = 30/18768x^2 -30

This question is confusing me so much, I might just work on the next one instead

@silk flame I think I got this answer correct, would you mind checking it?

I got

f(x) = 6/45 (x - 15)^2 + 30

Thanks so much for all your help @silk flame