Completing the square

Hi, please could someone help me with this question?

y=3x^2 - 30x - 6
By completing the square, find the coordinates of A on the graph (A is the turning point).

Thanks!

Reply 1

IHateChickens

9

3(x^2-10)-6 = 0
3(x-5)^2-75-6 = 0
3(x-5)^2-81 = 0
turning point is (5,-81)

(edited 1 year ago)

Reply 2

Pineapple27272

OP

7

Ohh I get it now, thanks.
I didn’t multiply the 25 by 3 so kept getting -31.

Reply 3

Kallisto

Entertainment Forum Helper

22

Original post by SMFreeze

3(x^2-10)-6 = 0
3(x-5)^2-75-6 = 0
3(x-5)^2-81 = 0
turning point is (5,-81)

Your approach is right, but your calculation has a mistake! First I divided the square term by 3:

x² - 10x - 2 = 0

then completing the square. As it is p = -10, completing the square in turn is (-10 : 2)² = 25 = 5², so:

x² -10x + 5² - 2 = 5² <=>
x² -10x + 5² - 5² - 2 = 0

And then it comes to the binomial term:

(x - 5)² - 25 - 2 = 0

Maybe you made a typo, because it is not -75, but -25.

(edited 1 year ago)

Reply 4

mqb2766

21

Original post by Kallisto

Your approach is right, but your calculation has a mistake! First I divided the square term by 3:

x² - 10x - 2 = 0

then completing the square. As it is p = -10, completing the square in turn is (-10 : 2)² = 25 = 5², so:

x² -10x + 5² - 2 = 5² <=>
x² -10x + 5² - 5² - 2 = 0

And then it comes to the binomial term:

(x - 5)² - 25 - 2 = 0

Maybe you made a typo, because it is not -75, but -25.

Subbing x=5 into the original quadratic gives y=-81, so #2 is ok.
If you divide the quadratic by 3 before completing the square, youve also divided the ymin value by 3 as well.

Reply 5

IHateChickens

9

🧢

Original post by Kallisto

Your approach is right, but your calculation has a mistake! First I divided the square term by 3:

x² - 10x - 2 = 0

then completing the square. As it is p = -10, completing the square in turn is (-10 : 2)² = 25 = 5², so:

x² -10x + 5² - 2 = 5² <=>
x² -10x + 5² - 5² - 2 = 0

And then it comes to the binomial term:

(x - 5)² - 25 - 2 = 0

Maybe you made a typo, because it is not -75, but -25.

🧢

Reply 6

Kallisto

Entertainment Forum Helper

22

Original post by mqb2766

Subbing x=5 into the original quadratic gives y=-81, so #2 is ok.
If you divide the quadratic by 3 before completing the square, youve also divided the ymin value by 3 as well.