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October 22, 2014

October 22, 2014

Posted by **David** on Tuesday, May 4, 2010 at 8:56pm.

"A quadratic function in the form f(x)=ax^2+bx+c contains the points (-1,0), (0,2), and (2,0)."

a) determine the values of a,b, and, c

b) Factorise the expression ax^2+bx+c obtained from the function in part (a)

please help! i've tried EVERYTHING :(

- Math -
**MathMate**, Tuesday, May 4, 2010 at 9:12pmLet

f(x)=ax^2+bx+c

from (-1,0), we conclude that

f(-1)=0, or

a(-1)^2 + b(-1) + c = 0......(1)

Similarly, from (0,2), we have

a(0)^2 + b(0) + c = 2........(2)

and from (2,0), we get

a(2)^2 + b(2) + c = 0........(3)

By solving the system of linear equations (1),(2) and (3), you will find the values of a,b and c.

After substituting the numerical values of a,b and c into f(x), you can factorize as required in question (c).

Note: the system of linear equations is easy to solve because if you examine equation (2), it reduces to c=2.

By substituting the value of c in (1) and (3), you only have to solve a system of 2 equations with two unknowns (a and b).

- Math -
**Damon**, Wednesday, May 5, 2010 at 4:01amA quadratic function in the form f(x)=ax^2+bx+c contains the points (-1,0), (0,2), and (2,0)."

Another way

y = (x+1)(x-2)(k)

2 = (1)(-2)(k)

2 = -2k

k = -1

so

y = (x+1)(x-2)(-1) (factored already)

so

y = -x^2 + x + 2

y =

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