Question

The function,
f(x) = x² - bx - 2b (where b is a positive constant),
after completing the square...
f(x) = ( x - (b/2) )² - 2b - (b²/4).
can i know why is (b/2) the line of symmetry of the graph ? how does this come about ?
The minima of the graph becomes ( b/2, - 2b - (b²/4) )

Answer 1

swag

Answer 2

You understand how to get to f(x) = )x-(b/2))^2 -(b^2/4) , right? Just the symmetry part?

Answer 3

yes jus the symmetry part, i only know y = mx + c @.@

Answer 4

im confuse about the mathematical law/rule that from Completing the square we can find the coordinates of maximum/minimum O:

Answer 5

have you learned about conics yet?

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

Answer 6

hmm.. not sure o.o

Answer 7

this is a general picture of axis of symmetry.
Definition is that axis of symmetry divides the parabola into two perfect, identical havles.

http://www.mathwarehouse.com/geometry/parabola/images/picture-of-axis-of-symmetry-thumb.png

lemme know if anything confuses you

Answer 8

uh ok ty :)

Answer 9

axis of symmetry is always a straight, vertical line.

let's start with the easiest example: y= x^2
http://www.bbc.co.uk/schools/gcsebitesize/maths/images/graph_24.gif

by looking at the graph, can you tell me what's the equation for the axis of symmetry?

x=?

Answer 10

0

Answer 11

good, :)

now are you familiar with translations?

Answer 12

yup

Answer 13

let's try this one for example.
find axis of symmetry of the blue line y= (x-2)^2
http://900igr.net/datai/algebra/Grafik-funktsii-Y-X/0004-004-Takim-obrazom-grafik-funktsii-yx-22-mozhet-byt-poluchen-iz.png

Answer 14

x=2

Answer 15

oh I should have covered up the answer xDD

Answer 16

oic! i think i get it

Answer 17

so it comes from translation

Answer 18

thank you study100 xD

Answer 19

Yes, since y= (x-2)^2 is a graph of x^2 that shifts right 2 units, the line of symmetry also shifts 2 units.

And yes it does involve translation :)

Answer 20

if you have time, I suggest you starting to learn conics section: parabola. It will make completing the squares/ finding maximum /minimum and such 100x easier.

These are very helpful tutorials , watch from1 to 4

https://www.khanacademy.org/math/algebra2/conics_precalc/parabolas_precalc/v/parabola-intuition-example-1

feel free to lemme know whenever you need help with this :)

Answer 21

btw, do you know how to find vertex?

vertex is the lowest or highest point in a parabola, which is max/min of the quadratic equation.

Answer 22

uhm.. sorry i dont know =.=

Answer 23

ok thanks

Answer 24

this site has the perfect way of explaining parabolas. This is all you really need to know about vertex

http://www.mathwarehouse.com/geometry/parabola/vertex-of-a-parabola.php

Answer 25

by using the formula to find axis of symmetry x= b/2a

use that x,
plug x in the orginal ax^2 + bx + c (for ex)
and find y.

then that order pair (x,y) is your vertex.

Answer 26

plug the x of axis symmetry ***