Question

Using complete sentences, explain how to convert your birthday function into standard form.

Answer 1

My birthday function: f(x) = 2(x-11)^2 + 27

Answer 2

standard form is
y(x) = a x^2 + b x + c

where a, b, and c are numbers.

the first step is "expand" (x-11)^2 = (x-11)(x-11) (you should have born in january.. you would have an easier problem)

Answer 3

lol sorry for not being born in january xD

Answer 4

So first we expand it to (x-11)^2 = (x-11)(x-11)?

Answer 5

use FOIL (for example) to multiply it out. combine like terms. add in the +27
and you will have standard form

Answer 6

so its like -11*-11 = 121
like four times lol?

Answer 7

see http://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-binomials
it explains it pretty well

Answer 8

I'm confused because theres like 3 terms instead of four? or does the exponent count as one?

Answer 9

The first step is to multiply
(x-11)(x-11)
the video will explain it faster (about 3 minutes) than we can do it by typing here...

Answer 10

@phi Can you help me? I need help on a question

Answer 11

(x-11)^2 = (x-11)(x-11)
so (x-11)(x-11)
x * x + x * (-11) + (-11) * x + (-11) * (-11)?

Answer 12

@phi

Answer 13

yes. x*x is written in short-hand as x^2 (x^2 means x*x)
x^2 + x * (-11) + (-11) * x + (-11) * (-11)

x*(-11) is written -11x (order does not matter when multiplying
and (-11)*x is written -11x (algebra leaves out the * sign)
of course -11*-11= 121
x^2 - 11x - 11 x + 121
now combine the "like terms" -11 x's and take away another 11 x's , how many x's ?

Answer 14

so after FOIL my equation should of been x^2 - 11x - 11 x + 121?

Answer 15

you still should combine -11x - 11x

Answer 16

x^2 - 11x - 11 x + 121
combine like terms...
x^2 - 11x^2 + 121?

Answer 17

you only get x^2 by multiplying

maybe its clearer if we had x + x
if you have 1 x and add another x you get 2 x's or 2x
it works the same with negative numbers
x - 2x
if you have 1 x and take away 2 x's you get -1 x
-11x - 11 x is the same idea: -11 x's take away 11 x's = -22 x

Answer 18

Alright I gotcha

Answer 19

so x^2 - 22x + 121?

Answer 20

yes.

we started with
f(x) = 2(x-11)^2 + 27

you expanded (x-11)^2 = (x-11)(x-11) = x^2 - 22x + 121

replace (x-11)^2 in your formula with the expanded version (be sure to use parens)

f(x)= 2(x^2 - 22x + 121) + 27

next step is distribute the 2. that means multiply every term inside the parens by 2

Answer 21

f(x)= 2(x^2 - 22x + 121) + 27
f(x) =(2x^2 - 44 + 242 + 54)?

Answer 22

first the x does not disappear in 2*(-22)x
second, the 27 is not part of (x-11)^2. You leave it alone.

Answer 23

remember we are doing
2(x-11)^2

which is the same as
2(x^2 - 22x + 121)

the +27 is added in later

Answer 24

my bad on the 44 without x, I didnt see the x earlier
f(x)= (2x^2 - 44x + 242) + 27

Answer 25

@Brad1996 Check out this thread: http://openstudy.com/study#/updates/52570bd1e4b0ede9e447371c

Answer 26

last step, we can drop the parens. (there is nothing "out front" multiplying them, so it is ok)
f(x)= 2x^2 - 44x + 242+ 27
last step
simplify by "combining like terms"... in this case the last two numbers can be added together.

Answer 27

yes, looks good