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.
+14995 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.
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\(y=ax^2+bx+c\) \(y=x^2+2x\)
\(3=9a-3b+c\\ 3=a+b+c\\ 0=0+0+c\)
\(c=0\)
\(9a-3b=a+b\\ 8a-4b=0\ |\ \cdot 3\\ \underline{9a-3b=3}\ |\ \cdot 4\)
\(24a-12b=0\\ \underline{36a-12b=12}\\ 12a=12\)
\(a=1\)
\(3=a+b+c\\ \underline{3=1+b+0}\)
\(b=2\)
\({\color{blue}100a+10b+c}=100\cdot 1+10\cdot 2+0\color{blue}=120\)
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