Question

“To pass by me you must tell me how to convert standard form into the general, vertex form... I have a test on it next week.”

Answer 1

Explain how to convert f(x) into the general, vertex form of the equation. Use complete sentences. You may use the f(x) you created in question 1 as an example.

Answer 2

my f(x) = x^2 + 10x + 16

Answer 3

do you know how to complete the square ?

Answer 4

That's with using the quadratic formula?

Answer 5

no...
its like squaring the half of co-efficient of x

Answer 6

Ok, How would I do that?

Answer 7

f(x) = x^2 + 10x + 16
whats the co-efficient of x ?

Answer 8

10? Because it's before x?

Answer 9

yes

Answer 10

now divide it by 2 and square it
what u get ?

Answer 11

25?

Answer 12

yes
so add and subtract 25 on right side
(x^2+10x +25) + 16-25

did u get what i did ?q

Answer 13

ok...
(x^2 + 10x +25) - 9
I don't think I did that right, do I remove the parenthesis?

Answer 14

i kept the paranthesis
so that it becomes easy to identify that it is a perfect square trinomial

Answer 15

y = (x+5)^2 - 9

Answer 16

Oh ok, I see where you got that, and this is already the vertex form? Do I have to put the 'a' variable on the outside?

Answer 17

if you need to find 'a' then put 1 outside, because a comes out to be =1

y= a (x-h)^2 +k

y= (x+5)^2 -9

a=1
h= -5
k = -9

Answer 18

got it ?
y= (x+5)^2-9 is your vertex form :)

Answer 19

Oh! Ok, cool, I understand that!:) Thanks so much! By the way, do you also know with standard form, how I would find the solutions for that? Just a quick question.

Answer 20

whats the standard form ?

Answer 21

ax^2 + bx + c

Answer 22

f(x) = x^2 + 10x + 16
is already in that form
a= 1
b=10
c=16

Answer 23

Yes, but would there be a way to find the 'solutions' for that equation?

Answer 24

oh, you need solution for f(x) ?? [but the question didn't ask for it....]
so f(x) = 0
x^2+10x +16 =0
know factor method ?

Answer 25

not actually
can u tell me 2 numbers whose sum is 10
and product = 16

Answer 26

2 and 8?

Answer 27

yes
so
x^2+8x +2x +16 =0
know how to proceed ? factor

Answer 28

No, I'm not sure, this would be factoring it out into two sets of parenthesis, right?

Answer 29

Something like (x+8) (x + 2)?

Answer 30

its like this
x (x+8) +2 (x+8) = 0
(x+8) (x+2) = 0

x+8 =0 or x+2 = 0
x= -8 or x= -2
thats it!

Answer 31

yes, you were correct :)

Answer 32

Oh, cool! Thanks! You've really helped! And thanks for the medal:)

Answer 33

welcome ^_^