Question

write y=3x^2+18x+25 in vertex form. Please explain how you do this.

Answer 1

y=3x^2+18x+25

y-25=3x^2+18x

y-25=3(x^2+6x)

y-25=3(x^2+6x+9-9)

y-25=3((x+3)^2-9)

y-25=3(x+3)^2-27

y=3(x+3)^2-27+25

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

The equation is now in vertex form y = a(x-h)^2 + k where a = 3, h = -3 and k = -2

So the vertex is (-3, -2)

Answer 2

Where did the 9's come from in y-25=3(x^2+6x+9-9)?

Answer 3

I took half of 6 in 6x to get 3.

Then I squared 3 to get 9.

I then added and subtracted 9 inside the parenthesis

Answer 4

I have a test on this stuff tomorrow so i want to fully understand how to do the problems.

Answer 5

I'm doing all this so I can get x^2+6x+9 which factors to (x+3)^2

Answer 6

Post another and you do the steps and I'll see if you did it correctly or not

Answer 7

Okay thanks a lot.

Answer 8

yw

Answer 9

wouldn't the 9's cancel out?

Answer 10

they do (if you're going backward). The idea is that we don't want to change the right hand side

So adding 9-9 (which is really 0) keeps things in balance

Answer 11

Okay is there a simpler way to do this? lol

Answer 12

the reason why i picked on 9 is because

(x+3)^2 = x^2 + 6x + 9

Answer 13

we have x^2+6x, which is missing that +9

but we can't just add 9 because that will change the equation, so we have to subtract 9 as well

Answer 14

Here's an alternative way

Answer 15

vertex form is y = a(x-h)^2 + k where (h,k) is the vertex

Answer 16

Im sorry for being such a pain.

Answer 17

To find h, which is the x coordinate of the vertex, use the formula

h = -b/(2a)

Answer 18

In the case of y=3x^2+18x+25, a = 3, b = 18 and c =25

So...

h = -b/(2a)

h = -18/(2*3)

h = -18/6

h = -3

Answer 19

We now can say that

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

becomes

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

y = 3(x+3)^2 + k

after we plug in a = 3 and h = -3

Answer 20

with me so far?

Answer 21

yeah so far

Answer 22

to find k, the last piece of info, we just plug the x coordinate of the vertex in for x

So plug in x = -3 into the original equation to get

y=3x^2+18x+25

y=3(-3)^2+18(-3)+25

y=3(9)+18(-3)+25

y=27-54+25

y = -2

So the y coordinate of the vertex is y = -2

This means k = -2

So we can go from

y = 3(x+3)^2 + k

to

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

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

Answer 23

The basic steps are:

Step 1) Find the x coordinate of the vertex using the formula

x = -b/(2a)

This will give you the value of 'h'

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Step 2) Then use this x coordinate of the vertex to find the y coordinate of the vertex to obtain k.

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Step 3) Plug the values of 'a', h and k into y = a(x-h)^2 + k to complete the square and get the original equation into vertex form

Answer 24

okay that helped me so much more. Thanks soooo much your awesome!

Answer 25

you're welcome