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Nonlinear Functions

SAT Math· difficulty 5/5

The graph of f(x)=ax3+bx2+cx+df(x) = ax^3 + bx^2 + cx + d crosses the x-axis at x=−2,0,3x = -2, 0, 3 and passes through (1,−6)(1, -6). What is aa?

  • A

    22

  • B

    −2-2

  • C

    −1-1

  • D

    11

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Explanation

f(x)=ax(x+2)(x−3)f(x) = a x(x+2)(x-3). f(1)=a(1)(3)(−2)=−6a=−6⇒a=1f(1) = a(1)(3)(-2) = -6a = -6 \Rightarrow a = 1.

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