quadratic functions in standard form (completing square)

stephanini · **Joined:** Tue, 24 Apr 2012 03:31:16 UTC **Posts:** 6

Write the quadratic function in standard form. Identify vertex, axis of symmetry and sketch graph.
y= -x^2+16x-5

standard form: f(x)= -x^2+16x-5
= -(x^2+16x+64-64)-5
= -(x^2+16x+64)-64 -5
Here is where I get confused...
= -(x^2+16x+64) -69 (?)
=-(x+8)(x+8)-69
multiply thru to rid the - sign out front
= (x-8)^2+69

However according to the markings on my test it should be
=(x-8)^2+59
Which would mean the Vertex is (8,59)
axis:x=8
graph...yadda yadda..... is it really 59? Just wondering where exactly I screwed up here. lol

Shadow · **Posted:** Wed, 25 Apr 2012 22:18:11 UTC

stephanini wrote:

Write the quadratic function in standard form. Identify vertex, axis of symmetry and sketch graph.
y= -x^2+16x-5

standard form: f(x)= -x^2+16x-5
= -(x^2+16x+64-64)-5 $\qquad$ This is where it goes wrong
= -(x^2+16x+64)-64 -5
Here is where I get confused...
= -(x^2+16x+64) -69 (?)
=-(x+8)(x+8)-69
multiply thru to rid the - sign out front
= (x-8)^2+69

However according to the markings on my test it should be
=(x-8)^2+59
Which would mean the Vertex is (8,59)
axis:x=8
graph...yadda yadda..... is it really 59? Just wondering where exactly I screwed up here. lol

Yes, when you factored out the minus sign, you didn't turn anything but the x^2

to the opposite sign. What you should have is -(x^2-16x+64-64)-5[tex] and then you go from there. The 59 comes from the fact that when you pull your other -64 out, it keeps a minus sign from the outside as well, so you get:

[tex]-(x^2-16x+64)+64-5

-(x^2-16x+64-64)-5[tex] and then you go from there. The 59 comes from the fact that when you pull your other -64 out, it keeps a minus sign from the outside as well, so you get:

[tex]-(x^2-16x+64)+64-5

stephanini · **Joined:** Tue, 24 Apr 2012 03:31:16 UTC **Posts:** 6

ohh ok I hate negatives they always mess me up.
Thank you!

got another one coming shortly if ya wanna figure that one out too

Shadow · **Posted:** Wed, 25 Apr 2012 22:43:23 UTC

stephanini wrote:

ohh ok I hate negatives they always mess me up.
Thank you!

got another one coming shortly if ya wanna figure that one out too

Be sure to show your work again and post it in another topic, and I will take a look.

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quadratic functions in standard form (completing square)

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