Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,4), vertical axis of symmetry, and contains the point (1,0).
What is (a , b, c)?
+14995 Suppose that we have an equation y = ax^2 + bx + c whose graph is a parabola with vertex (3,4), vertical axis of symmetry, and contains the point (1,0).
What is (a , b, c)?
Hello Guest!
\( y = ax^2 + bx + c\\ V(3,4)\\ P_1(1,0)\\ \color{blue}P_2(5,0)\)
\( y = ax^2 + bx + c\\ 4 = 9a + 3b + c\\ 0 = a + b + c\\ 0 = 25a + 5b + c\)
\(4 = 9a + 3b + c\\ \underline{0=9a+9b+9c}\\ 4=-6b-8c\\ \color{blue}2=-3b-4c\)
\(0=25a+25b+25c\\ \underline{0=25a+\ 5b\ +\ c}\\ \color{blue}0=20b+24c\)
\(12=-18b-24c\\ \underline{\ 0\ =\ 20b\ +\ 24c}\\ 12=2b\)
\(\ b\ =\ 6\)
\(0=20b+24c\\ c=-20b/24\\ c=-120/24\)
\(b=\ 6\)
\(c =\ -5\\ a=\ -1\)
\(y = ax^2 + bx + c\\ \color{blue}y=-x^2+6x-5\)
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