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### #1louisa567

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Posted 30 November 2006 - 08:35 PM

By writing f(x) = 3x^2 - 15x + 11 in the form a(x+b)^2 + c, find the coordinates of the min turning point.

Im really not sure about these questions.

Ive got as far as writing it as 3(x^2 - 5x) + 11. Is this in the right form? How can i go any further?

### #2John

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Posted 30 November 2006 - 09:06 PM

In this case i would use calculus first to find the turning point.

Then solve

3x - 15x + 11= a(x+b) + c

for a.

### #3louisa567

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Posted 30 November 2006 - 09:16 PM

Thanks john i also have another quick question.

When sketching y = x^3 + 3x^2 - 9x + 15 i cant seem to get any factors of 15 when using synthetic division. I dont know where i am going wrong!

### #4John

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Posted 30 November 2006 - 10:03 PM

Use the discriminant firstly to see if the roots are real and distinct (2 roots), equal(1 root) or imaginary(no roots).

and after that try using to 2 nearest factors of 15 both positive and negative factors.

### #5Untouchable

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Posted 01 December 2006 - 10:30 AM

QUOTE(louisa567 @ Nov 30 2006, 08:35 PM)

By writing f(x) = 3x^2 - 15x + 11 in the form a(x+b)^2 + c, find the coordinates of the min turning point.

Im really not sure about these questions.

Ive got as far as writing it as 3(x^2 - 5x) + 11. Is this in the right form? How can i go any further?

Writing f(x) = 3x² - 15x + 11 in the form a(x+b)² + c is the process of "completing the square".
This process can only work when the co-efficient (the number in front) of x² is 1.

Therefore re-aarange the function
f(x) = 3x² - 15x + 11
= 3(x² - 5x) + 11

Now try and "force" the square out of (x² - 5x) part.
= (x - 2.5)² - 2.5²
= (x - 2.5)² - 6.75

substitute this back into = 3(x² - 5x) + 11
= 3((x - 2.5)² - 6.25) + 11
= 3(x - 2.5)² - 18.75 + 11
= 3(x - 2.5)² - 7.75
f(x) = 3x² - 15x + 11 is now the form a(x+b)² + c

from this you can quickly get the turning point of the quadratic function

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