# SOLUTION: determine the quadratic function of f whose vertex is (4,3) and passes through (3,1) put in f(x)=ax^2+bx+c form

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 Click here to see ALL problems on Rational-functions Question 626766: determine the quadratic function of f whose vertex is (4,3) and passes through (3,1) put in f(x)=ax^2+bx+c formAnswer by nerdybill(6958)   (Show Source): You can put this solution on YOUR website! determine the quadratic function of f whose vertex is (4,3) and passes through (3,1) put in f(x)=ax^2+bx+c form "Vertex form" of a quadratic: y = a(x-h)^2 + k the problem gives us everything except the 'a'. Plug in given info and solve for 'a': y = a(x-h)^2 + k 1 = a(3-4)^2 + 3 1 = a(-1)^2 + 3 1 = a(1) + 3 1 = a + 3 -2 = a . so now we have: y = -2(x-4)^2 + 3 . Now, we reorganize to the right form: y = -2(x-4)^2 + 3 y = -2(x-4)(x-4) + 3 y = -2(x^2-8x+16) + 3 y = -2x^2+16x-32 + 3 y = -2x^2+16x-29 (this is the form they want)