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I had a hard time completing the square of some problems. This is what I did with them, I would appreciate if someone could show me the mistake that im doing and the right process in order to solve these problems.

Also, here there is an article about completing the square for anyone that dosent remeber about it.

http://www.uncwil.edu/courses/mat111hb/Izs/asolve/asolve.html#compsqr [Broken]

First problem

Complete the square on y = 3xsquare - x + 1 to write it in the form y = a (x - h)square +k

y = 3xsquare - x +1

3xsquare/3 and - x/3 =

3 (xsquare - 1/3x) +1

(1/3)square = 1/9

3 (xsquare -1/3x + 1/9) + 1 - 1/3

The answer is y = 3 (x + 1/3) square 2/3

But the answer on my book is y = 3 (x - 1/6) square + 11/12

I d like to know what was wrong there.

Second problem

Complete the square on y = xsquare - 6x + 10 to write it in the form y = a (x -h)square +k

y = xsquare - 6x + 10

(xsquare -6x) + 10

(-6/2)square = 9

(xsquare - 6x + 9) 10 - 9

The answer is (x + 3)square + 1

However on my book the aswer is y = (x - 3)square + 1

I dont really know where did that "-3" came from.

Third problem

-What are the x- and y- intercepts for f(x) = 2xsquare + x - 6 ?

This quadratic funtions is in the form " axsquare + bx + c " so I used the formula " h = -b/2a "

in order to solve it.

a = 2 and b = 1 on the function

so h = -1/2(2) = -1/4

k = 2(-1/4) square + (-1/4) - 6

k = 1/8 - 1/4 - 6

k= 49/8

I would appreciate if anyone is able to tell me how to solve these 3 problems.

Thanks a lot in advance.

Also, here there is an article about completing the square for anyone that dosent remeber about it.

http://www.uncwil.edu/courses/mat111hb/Izs/asolve/asolve.html#compsqr [Broken]

First problem

Complete the square on y = 3xsquare - x + 1 to write it in the form y = a (x - h)square +k

y = 3xsquare - x +1

3xsquare/3 and - x/3 =

3 (xsquare - 1/3x) +1

(1/3)square = 1/9

3 (xsquare -1/3x + 1/9) + 1 - 1/3

The answer is y = 3 (x + 1/3) square 2/3

But the answer on my book is y = 3 (x - 1/6) square + 11/12

I d like to know what was wrong there.

Second problem

Complete the square on y = xsquare - 6x + 10 to write it in the form y = a (x -h)square +k

y = xsquare - 6x + 10

(xsquare -6x) + 10

(-6/2)square = 9

(xsquare - 6x + 9) 10 - 9

The answer is (x + 3)square + 1

However on my book the aswer is y = (x - 3)square + 1

I dont really know where did that "-3" came from.

Third problem

-What are the x- and y- intercepts for f(x) = 2xsquare + x - 6 ?

This quadratic funtions is in the form " axsquare + bx + c " so I used the formula " h = -b/2a "

in order to solve it.

a = 2 and b = 1 on the function

so h = -1/2(2) = -1/4

k = 2(-1/4) square + (-1/4) - 6

k = 1/8 - 1/4 - 6

k= 49/8

I would appreciate if anyone is able to tell me how to solve these 3 problems.

Thanks a lot in advance.

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