SOLUTION: What is a quadratic function in standard form having zeros of 9 and -5? Thank you

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: What is a quadratic function in standard form having zeros of 9 and -5? Thank you      Log On


   



Question 1119340: What is a quadratic function in standard form having zeros of 9 and -5?
Thank you

Answer by ikleyn(52751) About Me  (Show Source):
You can put this solution on YOUR website!
.
For example, and as the simplest example, this function  q(x) = (x-9)*(x-(-5)),


which is equal to 


    q(x) = (x-9)*(x+5) = x%5E2+-9x+%2B+5x+-+45 = x%5E2+-+4x+-+45.



In more general situation, if you are asked to write the most general form of a quadratic function having the roots x%5B1%5D and x%5B2%5D, 

then such a function is 


    q(x) = a%2A%28x-x%5B1%5D%29%2A%28x-x%5B2%5D%29,


where "a" is the leading coefficient, which can be any non-zero real number. 

If you open parentheses and make all necessary multiplications and combine like terms, you will get


    q(x) = ax%5E2+-+a%2A%28x%5B1%5D%2Bx%5B2%5D%29+%2B+a%2Ax%5B1%5D%2Ax%5B2%5D.

Explained and solved.