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A parabola with equation  y=ax^2+bx+c contains the points (-3,3), (1,3), and (0,0). Find the value of 100a+10b+c.

 Oct 27, 2020
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A parabola with equation y=ax^2+bx+c contains the points (-3,3), (1,3), and (0,0). Find the value of 100a+10b+c.

 

Hello Guest!

 

\(y=ax^2+bx+c\)         \(y=x^2+2x\) 

 

\(3=9a-3b+c\\ 3=a+b+c\\ 0=0+0+c\)

\(c=0\)

\(9a-3b=a+b\\ 8a-4b=0\ |\ \cdot 3\\ \underline{9a-3b=3}\ |\ \cdot 4\)

\(24a-12b=0\\ \underline{36a-12b=12}\\ 12a=12\)

\(a=1\)

\(3=a+b+c\\ \underline{3=1+b+0}\)

\(b=2\)

 

\({\color{blue}100a+10b+c}=100\cdot 1+10\cdot 2+0\color{blue}=120\)

laugh  !

 Oct 27, 2020

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