Math Is Fun Forum

glenn101

Member

Registered: 2008-04-02

Posts: 108

Polyomials and simultaneous equations graphs

Ok, I need help with both polynomials and graph related questions.

Here are my polynomial questions.

Express x^2 in the form c(x+2)^2+a(x+2)+d

and

Express x^3 in the form (x+1)^3+a(x+1)^2+b(x+1)+c

and

Find the values of a,b and c such that x^2=a(x+1)^2+bx+c

and this is my graph related question.

Find the coordinates of the points of intersection for each of the following.

x^2+y^2=178
x+y=16

could you please try and explain them in depth as I am going to be tested on similar questions to this on Wednesday.

Thanks in advance,
Glenn.

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"If your going through hell, keep going."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Polyomials and simultaneous equations graphs

Questions 1, 2, and 3 are all identity questions (:P). An identity is where the Left hand side = Right hand side for any value of x. (the three horizontal lines where the equal sign should be is the sign of an identity)

All you have to do is expand the RHS until it is in the same form as the LHS and equate coefficients:

i.e.

So

Then you can easily solve and restate the problem with the solved values and you're done!

Try the others yourself.

For your 4th question, in the second equation solve for either x or y. I'll solve for y:

Then you can substitute into the first:

Now when x = 3,   y = 16-(3)=13

And when x=13,    y = 16-(13)=3

So the coordinates of intersection are (3,13), (13, 3)

Last edited by Identity (2008-04-13 20:50:56)

glenn101

Member

Registered: 2008-04-02

Posts: 108

Re: Polyomials and simultaneous equations graphs

Thank you identity, that helps alot:D

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"If your going through hell, keep going."