Question

How do you go from standard form to vertex form?

Answer 1

do you have an example to work with?

Answer 2

Completing the square, assuming you're talking about a parabola.

Answer 3

y = 3x2 + 19x – 40

Answer 4

ok step 1 is to find the x coordinate of the vertex

Answer 5

you use this formula

x = -b/(2a)

in this case

a = 3
b = 19

Answer 6

tell me what you get

Answer 7

-19/6

Answer 8

good

Answer 9

now that you know the x coordinate of the vertex, you plug this into the original equation to find the y coordinate of the vertex

Answer 10

y = 3x^2 + 19x – 40

y = 3(-19/6)^2 + 19(-19/6) – 40

....
....
....

y = ???

Answer 11

-841/12 ??

Answer 12

you got it

Answer 13

so the equation

\[\large y = 3x^2 + 19x - 40\]

turns into

\[\large y = 3\left(x + \frac{19}{6}\right)^2 - \frac{841}{12}\]

after completing the square

Answer 14

remember that after completing the square and getting an equation into vertex form, you will have this basic form

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

where (h,k) is the vertex

Answer 15

Thank you so much! Do you think you could do another example?

Answer 16

sure

Answer 17

y = 2x2 - 12x + 22

Answer 18

a = ??
b = ??

Answer 19

a= 2 b=-12

Answer 20

x = -b/(2a)

x = ??

Answer 21

to be technical, it should be

h = -b/(2a)

h = ??

Answer 22

h=3

Answer 23

this is the x coordinate of the vertex (and the axis of symmetry)

Answer 24

plug it into the original equation to find the y coordinate of the vertex (ie the value of k)

Answer 25

throughout this whole process, 'a' stays the same and it is a = 2 in this case

Answer 26

-40=y

Answer 27

no, that's not correct

Answer 28

4

Answer 29

y = 2x^2-12x+22

y = 2(3)^2-12(3)+22

y = 4

correct

Answer 30

so vertex = (3,4)

Answer 31

x coordinate of the vertex is 3 ----> h = 3
y coordinate of the vertex is 4 ----> k = 4

Answer 32

a = 2 (given)
h = 3 (just found this)
k = 4 (just found this)


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


y = 2(x-3)^2 + 4 ... plug in a = 2, h = 3, k = 4


so


2x^2-12x+22


converts to


y = 2(x-3)^2 + 4


which is now in vertex form

Answer 33

THANK YOU SO MUCH! this helps tremendously! It's actually not that hard!

Answer 34

nope it's not too bad once you know a handy formula

you could go another route and complete the square, but that gets ugly sometimes

Answer 35

yeah that one is really confusing....I'll stick with this one:)