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# function help please

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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
+11086
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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!

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

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

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

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

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

$$a=\frac{1}{2}\\ b=\frac{3}{2}$$

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

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

$$f(3)=9$$

!

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