From the graph of f(x)= x^4 + x^3 – 13x^2 – x + 12 find the x and y intercepts.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation of the graph to be plotted and the x and y intercepts identified is f(x)= x^4 + x^3 – 13x^2 – x + 12

The x-intercept can be found by solving f(x) = 0, for values of x

x^4 + x^3 – 13x^2 – x + 12 = 0

=> x^4 + 4x^3 - 3x^3 - 12x^2 - x^2 - 4x + 3x + 12 = 0

=> x^3(x + 4) - 3x^2(x + 4) - x(x + 4) + 3(x + 4) = 0

=> (x + 4)(x^3 - 3x^2 - x + 3) = 0

=> (x + 4)(x^2(x - 3) - 1(x - 3)) = 0

=> (x + 4)(x - 3)(x^2 - 1) = 0

=> (x + 4)(x - 3)(x - 1)(x + 1) = 0

=> x = -4, x = 3, x = 1 and x = -1

The x-intercepts are (-4, 0), (-1, 0), (1, 0) and (3, 0)

The y-intercept can be found by finding f(x) for x = 0

f(0) = 0^4 + 0^3 – 13*0^2 – 0 + 12

=> 12

The y-intercept is (0, 12)

The required x-intercepts are (-4, 0), (-1, 0), (1, 0) and (3, 0) and the y-intercept is (0, 12)

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