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

$(h,k)=(-\frac{b}{2a},f(-\frac{b}{2a}))$

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

the vertex is

$\begin{gathered} h=-(\frac{-3}{2(-1)}) \\ h=-1.5 \end{gathered}$

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