Quadratic Polynomial

**Civy71** · February 19th 2013, 05:17 PM

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

**jakncoke** · February 19th 2013, 05:34 PM

$x^2$

**Civy71** · February 19th 2013, 05:42 PM

Thanks Dave, how did you arrive at that answer?

**jakncoke** · February 19th 2013, 05:46 PM

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.

**HallsofIvy** · February 19th 2013, 06:59 PM

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.

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