Question

Determine an equation in factored form for the function below:

Answer 1

The x-intercepts of the graph are at x = 1 twice and at x = -4/3

That is,

`\begin{gathered} x=1 \\ (x-1)=0 \\ x=1 \\ (x-1)=0 \\ \text{and x=}(-4)/(3) \\ 3x=-4 \\ (3x+4)=0 \\ \end{gathered}`
`\begin{gathered} \text{ The function is} \\ y=a(x-1)(x-1)(3x+4) \end{gathered}`

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