Function 3

Function f(x)=a(x-r)(x-s) the graph of the function has an x-intercept at (-4, 0) and (2, 0) and passes through the point (-2,-8). Find constant a, r, s.

Correct answer:

a =  1
r =  -4
s =  2

Step-by-step explanation:

$$\begin{gathered} f(x)=a(x-r)(x-s) \\ r=-4 \\ s=2 \\ -8=a\cdot (-2-r)\cdot (-2-s) \\ -8=a\cdot (-2-(-4))\cdot (-2-2) \\ 8a=8 \\ a=\frac{8}{8}=1 \\ a=1 \end{gathered}$$

$$\begin{gathered} s=2 \\ f(x)=(x+4)(x-2) \end{gathered}$$

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