The x-intercepts of the graph are at x = 1 twice and at x = -4/3
That is,
[tex]\begin{gathered} x=1 \\ (x-1)=0 \\ x=1 \\ (x-1)=0 \\ \text{and x=}\frac{-4}{3} \\ 3x=-4 \\ (3x+4)=0 \\ \end{gathered}[/tex][tex]\begin{gathered} \text{ The function is} \\ y=a(x-1)(x-1)(3x+4) \end{gathered}[/tex]
To find the value of a, we substituute the y-intecepts into the function
y - intercept = (0, 6)
that is when x = 0 , y=6
Substitute x = 0, y = 6 into the function
6= a(0-1)(0-1)(3(0) + 4)
6 = a(1)(1)(4)
6 = 4a
4a = 6
a = 6/4
a = 1.5
The equation in factored form is
1.5 (x- 1)(x - 1)(3x + 4) = 0
