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anonymous
 one year ago
Find the vertex of the graph of the function.
f(x) = 4x^2 + 24x + 32
anonymous
 one year ago
Find the vertex of the graph of the function. f(x) = 4x^2 + 24x + 32

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Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Basically you're taking your equation \(y=4x^2+24+32\) that has the quadratic form \(y=ax^2+bx+c\) and converting it into vertex form: \(y=a(xh)^2+k\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2So to start, we can immediately see that all the coefficients are divisible by 4. So simplify your function.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=4x2+24+32= y=ax2+bx+c ? = y=a(x−h)2+k right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=a(x−h)2+k = = y=4(x−h)2+k

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2You got the idea somewhat, but first lets simplify this :) You'll see what I mean by "fitting the equation into the form" :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah, kinda. what i don't get is how to get x&y values to then find h&k

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh and thank you so much for helping me @Jhannybean

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Simplify this: \[\large y=\frac{4}{4}x^2+\frac{24}{4}x+\frac{32}{4}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry mi wifi was acting up @Jhannybean

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=x2+6x+8 y=ax2+bx+c ? y=a(x−h)2+k

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but how will i get the other values?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Alright, now that we simplified it to \(y=x^2+6x+8\), we need to use the method of completing the square. Have you learned that method yet?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2In the method of completing the square, we will basically create another quadratic function into the quadratic function we already have, \(y=x^2+6x+8\) It's like an inception of quadratics that will help you find the vertex. :P

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2So let's work it out slowly. First set your function equal to zero. \(y=x^2+6x+8=0\) Next, move over your constants to one side of the equation, while leaving your variables on the other side side. \(y=x^2+6x=8\) Following so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do i get x and y intercepts?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Once we're dne you'll have your x and y intercepts and you'll see what I mean, just follow me on this one :P Trust!

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Now we're going to create a quadratic on the left hand side of the function by completing the square of the left hand side. Essentially we're going to `finish` the quadratic on the left hand side so it resembles the form \(ax^2+bx+c\) but right now, we've only got \(ax^2+bx\) and THEREFORE need to find ourselves a new \(c\) value.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[c=\left(\frac{b}{2}\right)^2 \longrightarrow c=\left(\frac{6}{2}\right)^2 = (3)^2 = 9\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Yep. So since we're `adding` c to the left side, we have to respectively add it to the right side as well

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[y=x^2+6x\color{red}{+9}=8\color{red}{+9}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=x2+6x+9=−8+9 y=x2+6x+9=+1

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2If you're good with simplifying quadratics, you'll see that the left hand side now is a PERFECT square! :o \(x^2+6x+9 \longrightarrow (x+3)^2\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Rewrite it. \[y=(x+3)^2=1\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Well, you would move the 1 over to fit your new equation to fit the vertex form \(y=a(x+h)^2+k\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Therefore \(y=a(x+h)^2+k \longrightarrow y=(x+3)^21\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Do you see how it works?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Whoop, I wrote it wrong, \(y=a(xh)^2+k\)** Typo.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=a(x−h)2+k⟶y=(x+3)2−1

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2So we know a positive can be split into 2 negatives, therefore \(y=a(xh)^2+k \longrightarrow y=(x(3))^21\)

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2So tell me, what are your x and y intercepts? :D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0xintercept = (x−(−3))2−1 = 1 = (x−(−3))2

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Im not understanding that.

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2\[y=a(x\color{red}{h})^2\color{blue}{+k} \longrightarrow y=(x\color{red}{(3)})^2\color{blue}{1}\]

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2To help you identify them a little better. the part in red is your xintercept, part in blue is your y intercept

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats much better, sorry i was confused

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y=a(x−h)^{2}+k⟶y=(x−(−3))^{2}−1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait so what do i do now? the intercepts?

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2You're toldto find the vertex of the graph, which I helped you find in the post above :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you @Jhannybean , sorry im a little heardheaded but i just reread it and i completely understand

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Awesome! Glad I could help :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Jhannybean sorry to bother you again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0does it mean that the answer would be "b"?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0use is formula....\[\frac{ b }{ 2a }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do i plug in a=1 and b=6??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=(x−(−3))^2−1 \[\frac{ 3 }{ 1 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1438666779185:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0a and b is coefficient

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be the 3,4 or 4,3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lowest point is obviously the yaxis

dan815
 one year ago
Best ResponseYou've already chosen the best response.1lisnten to me, do u know how transformations work with functions

dan815
 one year ago
Best ResponseYou've already chosen the best response.1do you know how transformations work??

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay how about completing the square

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0f(x3) = f(x) shifted 3 to the right as example

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if i am subtracing 3 away from what i am inputting at the time, then it must appear later by 3 units

dan815
 one year ago
Best ResponseYou've already chosen the best response.1f(x) = 4x^2 + 24x + 32 the point im trying to get across is we want to write this equation in the form f(x) = a(xb)^2+c this means the vertex is at (b,c)

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay forget that BS for now

dan815
 one year ago
Best ResponseYou've already chosen the best response.1do you get why this equation has vertex at b,c though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what i dont know is if it goes before or after the 4

dan815
 one year ago
Best ResponseYou've already chosen the best response.1no forget all that stuff, we are going to do this logically

dan815
 one year ago
Best ResponseYou've already chosen the best response.1f(x) = a(xb)^2+c do you get why the vertex for this equation is b,c

dan815
 one year ago
Best ResponseYou've already chosen the best response.1think about the base graph

dan815
 one year ago
Best ResponseYou've already chosen the best response.1how do you apply transformations to it?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1y=(xb)^2 would shift it b units to the right

dan815
 one year ago
Best ResponseYou've already chosen the best response.1y=(xb)^2 + c would shift it b units to the right and c units up

dan815
 one year ago
Best ResponseYou've already chosen the best response.1you can think about it like this too (yc)=(xb)^2 y shifted c up and x shifted b right

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0THIS MAN HAS CLEARLY LOST IT

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry my wifi wasn't working

dan815
 one year ago
Best ResponseYou've already chosen the best response.1do u get why the vertex for y=a(xb)^2+c is at (b,c) then?

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay then y=4x^2 + 24x + 32 rewrite this in that form

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=a(xb)^2+c y=4(x24)^2+32

dan815
 one year ago
Best ResponseYou've already chosen the best response.1expand the brackets see if u get the right equation

dan815
 one year ago
Best ResponseYou've already chosen the best response.1y=4(x24)^2+32 =4*(x24)(x24)+32 = 4*(x^248x+24^2)+32

dan815
 one year ago
Best ResponseYou've already chosen the best response.1its much bigger than before now

dan815
 one year ago
Best ResponseYou've already chosen the best response.1so we have to transform to the form we want properly

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so you did the square

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay ill show u how to do it this time, u can try to do it later

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0= 4*(x^248x+24^2)+32

dan815
 one year ago
Best ResponseYou've already chosen the best response.1y=4x^2 + 24x + 32 y=4(x^2+6x)+32 ill complete the square in the brackets =4(x^2+6x+99)+32 =4((x^2+6x+9)9)+32 =4*((x+3)^29)+32 =4*(x+3)^2+329*4 =4*(x+3)^2+3236 =4*(x+3)^24 so the vertex is at (3,4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0uhhhhh finally i understand

dan815
 one year ago
Best ResponseYou've already chosen the best response.1y=4x^2 + 32x + 32 tell me the vertex for this equation and i will believe you

dan815
 one year ago
Best ResponseYou've already chosen the best response.1follow the steps i went through up there, its a very similar question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@dan815 whoa you went thru all at

dan815
 one year ago
Best ResponseYou've already chosen the best response.1it looks like a lot of steps because im showing every little change, but normally once u learn the method u do it all in 1 or 2 steps

dan815
 one year ago
Best ResponseYou've already chosen the best response.1u can do these in ur head pretty much

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea ikr thats why i said that lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=4x^2 + 32x + 32 y=4(x^2+8x)+32 would it be that

dan815
 one year ago
Best ResponseYou've already chosen the best response.1thats a start now u have to complete the square in those brackets go on

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=4x^2 + 32x + 32 y=4(x^2+8x)+32 =4(x^2+8x+99)+32 =4((x^2+8x+9)9)+32 =4*((x+4)^29)+32 =4*(x+4)^2+329*4 =4*(x+4)^2+3236 =4*(x+4)^24

dan815
 one year ago
Best ResponseYou've already chosen the best response.1the question u are asking urself here is how can i get a perfect square out of x^2+8x

dan815
 one year ago
Best ResponseYou've already chosen the best response.1when u see x^2+8x you have to realize that the square has to be (x+4)^2 since this is the only square that will give u a x^2 and 8x now the constant is not there so we add and subtract that the constant part will be 4^2=16 so x^2+8x+1616

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so you have to multiply 8 by 2

dan815
 one year ago
Best ResponseYou've already chosen the best response.1u are not multiplying 8 by 2

dan815
 one year ago
Best ResponseYou've already chosen the best response.1u are dividing (8/2) then squaring (8/2)^2 = 16 just so happesn that its also the same as 8*2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0y=4x^2 + 32x + 32 y=4(x^2+8x)+32 =4(x^2+8x+1616)+32 =4((x^2+8x+16)16)+32 =4*((x+4)^216)+32 =4*(x+4)^2+3216*4

dan815
 one year ago
Best ResponseYou've already chosen the best response.1when u have x^2+ax and u want to write it in square form you take half of a as (x+a/2)^2=x^2+ax+(a/2)^2 ^ term on x works out

dan815
 one year ago
Best ResponseYou've already chosen the best response.1yes now u got it so what is the vertex

dan815
 one year ago
Best ResponseYou've already chosen the best response.1what is the constant term

dan815
 one year ago
Best ResponseYou've already chosen the best response.1=4*(x+4)^2+3216*4 simplfy this to a(xb)^2+c

dan815
 one year ago
Best ResponseYou've already chosen the best response.1=4*(x+4)^2+3216*4 =4*(x+4)^2+3264 =??

dan815
 one year ago
Best ResponseYou've already chosen the best response.1oaky so what is the vertex?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i keep thinking its 4,3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but i don't think it is that

dan815
 one year ago
Best ResponseYou've already chosen the best response.1what is the vertex for this equation =a(xb)^2+c

dan815
 one year ago
Best ResponseYou've already chosen the best response.1okay so what is the vertex for this =4*(x+4)^232

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that was really hard but now i got it lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0only the inside changes sign, its the opposite

dan815
 one year ago
Best ResponseYou've already chosen the best response.1no problem, try some completing the square excercises just to make sure though

dan815
 one year ago
Best ResponseYou've already chosen the best response.1or just do some expanding excercised, that should build your intuition up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i tried doing it with analytic geometry method lol

dan815
 one year ago
Best ResponseYou've already chosen the best response.1for the record here is a short cut

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would it be the same for Writing the quadratic function in vertex form. y = x2 + 8x + 18

dan815
 one year ago
Best ResponseYou've already chosen the best response.1f(x) = 4x^2 + 24x + 32 you take the middle number and divide by 2* the first number 24/(2*4) = 24/8=3 now plug 3 into equation f(3)=4*9+24*3+32=4 vertex is at (3,f(3)) = (3,4)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh wow that as much faster

dan815
 one year ago
Best ResponseYou've already chosen the best response.1since u do not understand it

dan815
 one year ago
Best ResponseYou've already chosen the best response.1not until you understand completing the square method, then u can derive this

dan815
 one year ago
Best ResponseYou've already chosen the best response.1and then u can derive it one more time after u learn about derivatives

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea i told him that stuff earlier lol b/2a

dan815
 one year ago
Best ResponseYou've already chosen the best response.1f(x)=ax^2+bx+c prove that the vertex is at (b/2a, ) x_coord=b/2a y_coord=f(b/2a) This can be your home work or something

dan815
 one year ago
Best ResponseYou've already chosen the best response.1hint complete square for f(x)=ax^2+bx+c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how can i rate a qualified helper

Jhannybean
 one year ago
Best ResponseYou've already chosen the best response.2Similar to my method without simplifying the equation first
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