# Math Help - Quadratic Polynomial

1. ## Quadratic Polynomial

Find the quadratic polynomial whose graph passes through the points (0,0) (-1,1) and (1,1).

2. ## Re: Quadratic Polynomial

$x^2$

3. ## Re: Quadratic Polynomial

Thanks Dave, how did you arrive at that answer?

4. ## Re: Quadratic Polynomial

I used solved the linear system 0 = f(0) = $a_3$ 1 = f(-1) = $a_2 - a_1 + a_0$ 1 = f(1) = $a_2 + a_1 + a_0$.
Then i looked at the question, the points and slapped my self on my forehead and erased all my work to save embarrassment.

5. ## Re: Quadratic Polynomial

Any "quadratic polynomial" can be written in the form $y= ax^2+ bx+ c$ for some numbers, a, b, and c. When x= 0, y= 0 so $0= a(0^2)+ b(0)+ c$ so c= 0. Then when x= -1, y= 1 so $1= a(-1)^2+ b(-1)$ or $a- b= 1$. Finally, when x= 1, y= 1 so $1= a(1)^2+ b(1)$ or a+ b= 1.

Solve the two equations a+ b= 1 and a- b= 1 for a and b.