Completing the square

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Complete the square on the function f(x) = –x2 + 2x –17 to obtain an equivalent function then identify the vertex.

I've been working on this one, but I i've never been any good at completing the square. May I have some help please?
 
Hello batbat,

For a function of the form

. . . . f(x) = ax<sup>2</sup> + bx + c

you can complete the square by adding and subtracting

. . . . b<sup>2</sup>/(4a)

from the function. For example, the function you wrote is:

. . . . f(x) = –x<sup>2</sup> + 2x – 17

which makes a = -1, b = 2, and c = -17. Thus:

. . . . b<sup>2</sup>/(4a) = -1

and you can add and subtract this from the function (in effect adding '0') to obtain:

complete.png


Can you identify the vertex?
 
Thank you!
One last little question...
Is the vertex -1,-16?
 
Hi batbat,

batbat said:
Thank you!
One last little question...
Is the vertex -1,-16?
I made a small mistake (which you should have caught, tsk :wink:). Try reloading the image (the final answer is fixed now). Sorry for any confusion!
 
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