Question

PARABOLA QUESTION!
Write the equation in standard form
Y=16x^2+32x+5

Answer 1

:o Looks like it is.

Answer 2

No, no parabola standard form

Answer 3

That is.
y = Ax^2 + Bx + C is standard form for a quadratic equation.

Answer 4

as in (x-h)^2=4p(y-k). I didn't ask for quadratic form.

Answer 5

Facepalm. That's not standard form.

Answer 6

If this helps, I have the answer: (x-1)^2=-1/16(y-21)

Answer 7

AWMIGAWD! I know what quadratic form is! I took that 3 years ago! This is "Standard form of Equations for parabolas".

Answer 8

http://www.mathwarehouse.com/geometry/parabola/standard-and-vertex-form.php

Answer 9

O.o

Answer 10

@ranga so how did they get (x-1)^2=-1/16(y-21) as an answer for this?

Answer 11

That is not the correct answer to this problem. They are two different parabolas.
There is some problem with this question. y = 16x^2 + 32x + 5 is already in standard form and they ask you to put it in standard form. Then you show the answer which is a different parabola than the one given. You can cross-multiply and simplify the answer and you won't get the original parabola.

I will try to put it in the vertex form by completing the square:
y = 16x^2 + 32x + 5
y = 16(x^2 + 2x + 5/16)
y = 16{ (x + 1)^2 - 1 + 5/16 }
y = 16{ (x+1)^2 - 11/16 }
y = 16(x+1)^2 - 11
This parabola has vertex at (-1, -11). It is an upright parabola that opens upward.

(The answer is an upside down parabola that opens downward.)

Answer 12

Gee, Thanks a lot man! How'd you complete the square so simply? I usually take up a whole page completing the square! @ranga

Answer 13

To complete the square of say, x^2 + 6x - 8
You divide the coefficient of x by 2: 6/2 = 3. This 3 will go within the square:
(x + 3)^2 Then you subtract 3^2
So x^2 + 6x - 8 = (x + 3)^2 - 3^2 - 8 = (x+3)^2 - 17

Answer 14

x^2 - 14x + 8 = (x - 7)^2 - 7^2 + 8 = (x-7)^2 - 49 + 8 = (x - 7)^2 - 41

Answer 15

Don't you have to add the (b/2)^2 to both sides as well?

Answer 16

If you have an equation: x^2 - 14x + 8 = 0 then you add (b/2)^2 to both sides.
But when you have just an expression (there are no two sides since there is no equal sign) then you subtract it.

Answer 17

Adding to the right is same as subtracting from the left.

Answer 18

Wait. I never fully understood this, I always asked my teacher and she would get pissed off, hopefully you don't see it as a stupid question too haha. How come, when you add and subtract b/2^2 from the same side it doesn't cancel out? :o

Answer 19

Example: Complete the square of x^2 + 14x - 3
Divide coefficient of x by 2: 14/2 = +7
This +7 will go inside the square: (x+7)^2. To understand why we subtract 7^2, expand (x+7)^2 and see what you get: (x+7)^2 = x^2 + 14x + 7^2. Compare this to what we started with: x^2 + 14x - 3. By squaring (x+7)^2, we have introduced an extra term 7^2 in the expansion of (x+7)^2. So we need to subtract 7^2.
x^2 + 14x - 3 = (x+7)^2 - 7^2 - 3 = (x+7)^2 - 49 - 3 = (x+7)^2 - 52

Answer 20

OHHHHHH! Wow. Thank you so much ranga. I really appreciate the time you spent helping me out.

Answer 21

You are welcome.