Use the partial factoring to determine two points and the vertex of  3x^2-x-4

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to convert the given quadratic in its factored form, using the following formula, such that:

`ax^2 + bx + c = a(x - x_1)(x - x_2)`

Since `x_(1,2)` represent the solutions to equation, you need to use quadratic formula to evaluate the solutions, such that:

`x_(1,2) = (1+-sqrt(1+48))/6 => x_(1,2) = (1+-7)/6`

`x_1 = 4/3 , x_2 = -1`

`3x^2 - x - 4 = 3(x - 4/3)(x + 1) => 3x^2 - x - 4 = (3x - 4)(3x + 3)`

You need to evaluate the coordinates of the vertex of parabola, using the following formulas, such that:

`x = -b/(2a), y = (4ac - b^2)/(4a)`

Identifying the coefficients a,b,c yields:

`x = 1/6`

`y = (-48 - 1)/12 => y = -49/12`

Hence, evaluating the factored form of quadratic equation yields `3x^2 - x - 4 = (3x - 4)(3x + 3)` and evaluating the coordinates of the vertex of parabola, yields `x = 1/6, y = -49/12.`

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