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# Suppose that we have an equation y = ax^2 + bx + c

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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)?

Oct 30, 2020

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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!

\( y = ax^2 + bx + c\\ V(3,4)\\ P_1(1,0)\\ \color{blue}P_2(5,0)\)

\( y = ax^2 + bx + c\\ 4 = 9a + 3b + c\\ 0 = a + b + c\\ 0 = 25a + 5b + c\)

\(4 = 9a + 3b + c\\ \underline{0=9a+9b+9c}\\ 4=-6b-8c\\ \color{blue}2=-3b-4c\)

\(0=25a+25b+25c\\ \underline{0=25a+\ 5b\ +\ c}\\ \color{blue}0=20b+24c\)

\(12=-18b-24c\\ \underline{\ 0\ =\ 20b\ +\ 24c}\\ 12=2b\)

\(\ b\ =\ 6\)

\(0=20b+24c\\ c=-20b/24\\ c=-120/24\)

\(b=\ 6\)

\(c =\ -5\\ a=\ -1\)

\(y = ax^2 + bx + c\\ \color{blue}y=-x^2+6x-5\)

!

\(\)

Oct 30, 2020
edited by asinus  Oct 30, 2020