# SOLUTION: Determine the quadratic function, f(x) = ax^2 + bx + c, whose vertex is (1, 8) and passes through the point (-3, 4)

Algebra ->  Algebra  -> Functions -> SOLUTION: Determine the quadratic function, f(x) = ax^2 + bx + c, whose vertex is (1, 8) and passes through the point (-3, 4)      Log On

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 Question 540835: Determine the quadratic function, f(x) = ax^2 + bx + c, whose vertex is (1, 8) and passes through the point (-3, 4)Answer by AnlytcPhil(1276)   (Show Source): You can put this solution on YOUR website!Determine the quadratic function, f(x) = ax^2 + bx + c, whose vertex is (1, 8) and passes through the point (-3, 4) ```It has the form f(x) = a(x - h)² + k where the vertex is (h,k), Since we are given that the vertex is (1,8), we have f(x) = a(x - 1)² + 8 Since the parabola passes through the point (x,y) = (-3,4), we will substitute -3 for x and since y = f(x) we will substitute 4 for f(x): 4 = a(-3 - 1)² + 8 4 = a(-4)² + 8 4 = a(16) + 8 4 = 16a + 8 -4 = 16a = a = a We substitute for a in f(x) = a(x - 1)² + 8 f(x) = (x - 1)² + 8 That is in vertex form. To get it in standard form f(x) = ax² + bx + c f(x) = (x - 1)(x - 1) + 8 f(x) = (x² - 2x + 1) + 8 f(x) = x² - ·2x + ·1 + 8 f(x) = x² + x - + 8 f(x) = x² + x - + 32/4 f(x) = x² + x + Edwin```