Question

13. Identify the zeros of f(x)= - x - 3x + 4 = -(x + 4)(x - 1).Sketch a rough graph of f(x).

Answer 1

`f(x)=(x+4)(x-1)`

To find the zeros of the function we equal the function to 0

`\begin{gathered} 0=-(x+4)(x-1) \\ 0=(x+4)(x-1) \end{gathered}`

since this is a product, it can be 0 when one of the factors is equal to zero, for that reason:

`\begin{gathered} x+4=0 \\ x=-4 \\ x-1=0 \\ x=1 \end{gathered}`

the zeros of the function are x=-4 and x=1.

after that to do the sketch find the vertex which can be found by

`(h,k)=(-(b)/(2a),f(-(b)/(2a)))`

according to the function a=-1, b=-3 and c=4

the vertex is

`\begin{gathered} h=-((-3)/(2(-1))) \\ h=-1.5 \end{gathered}`

using the function find k

`\begin{gathered} k=-(-1.5)^2-3(-1.5)+4 \\ k=6.25 \end{gathered}`

the vertex is at (-1.5,6.25)

the graph should look like this