Determine the quadratic function, f(x)=ax^2+bx+c, whose vertex is (-1, 7) and passes through the point (-3, -9).

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The vertex of the quadratic function f(x)=ax^2+bx+c is (-1, 7) and it passes through the point (-3, -9).

The function can be written as f(x) = a(x + 1)^2 + 7

=> a(x^2 + 2x + 1) + 7

=> ax^2 + 2ax + a + 7

And -9 = a*(-3)^2 + 2a*(-3) + a + 7

=> -9 = 9a - 6a + a + 7

=> -9 - 7 = 4a

=> -16 = 4a

=> a = -4

The required quadratic function is f(x) = -4x^2 - 8x + 3

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