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If f(0) = 0, f(1) = 2, f(2) = 5 ,  and ax^2+bx+c=0, what is the value of f(3)?

 

thanks!

 Oct 22, 2020
 #1
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If f(0) = 0, f(1) = 2, f(2) = 5 , and ax^2+bx+c=0, what is the value of f(3)?

 

Hello Guest!

 

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

 

\(\color{BrickRed}f(0)=0\\ \color{blue} c=0\)

 

\(\color{BrickRed}f(1)=2\\ a+b=2 \)

\(\color{BrickRed}f(2)=5\\ 4a+2b=5\)

\(b=2-a\\ 4a+2(2-a)=5\\ 4a+4-2a=5\\ 2a=1 \)

\(a=\frac{1}{2}\\ b=\frac{3}{2}\)

 

\(f(x)=\frac{1}{2}x^2+\frac{3}{2}x+0\)

 

\(f(3)=\frac{1}{2}\cdot 3^2+\frac{3}{2}\cdot 3\)

\(f(3)=9\)

laugh  !

 Oct 23, 2020
edited by asinus  Oct 23, 2020
edited by asinus  Oct 23, 2020

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