zeros: (-1,0) and (2,0)
Use the zeros to write the factors of the function as follow:
zeros: (b,0) and (c,0)
[tex]y=a(x-b)(x-c)[/tex][tex]\begin{gathered} y=a(x-(-1))(x-2) \\ y=a(x+1)(x-2) \end{gathered}[/tex]
Use the given oint (1,6) to find the value of a:
[tex]\begin{gathered} 6=a(1+1)(1-2) \\ 6=a(2)(-1) \\ 6=-2a \\ \frac{6}{-2}=a \\ \\ a=-3 \end{gathered}[/tex]
The function is:
[tex]y=-3(x+1)(x-2)[/tex]
Use FOIL method and distributive property to simplify:
[tex]\begin{gathered} y=-3(x*x-2*x+1*x-2*1) \\ y=-3(x^2-2x+x-2) \\ y=-3(x^2-x-2) \\ \\ y=-3x^2+3x+6 \end{gathered}[/tex]
Then, the function in the graph is y=-3x^+63x+6
Answer: D.
