Question

Can you help me with 22. How graph - do I randomly enter values for x to solve for y. How can I determine vertex without graphing. Isn’t there a way to figure out vertex without graphing? Thanks

Answer 1

The given function is:

`f(x)=(5)/(6)|x+3|-1`

The modulus function is a combination of a positive and a negative so let y=f(x) and get two equations as follows:

`\begin{gathered} y=(5)/(6)|x+3|-1 \\ y=(5)/(6)(x+3)-1;y=(-5)/(6)(x+3)-1 \end{gathered}`

Find the point of intersection of these two lines to get the vertex of the modulus function.

Subtract the second equation from the first to get:

`\begin{gathered} (5)/(6)(x+3)-1+(5)/(6)(x+3)+1=0 \\ x+3=0 \\ x=-3 \end{gathered}`

Substitute x=-3 to get:

`y=-1`

Hence (-3,-1) is the vertex of the function.

Graph the function as shown below:

Solve for y=0 as follows:

`\begin{gathered} (5)/(6)|x+3|-1=0 \\ (5)/(6)|x+3|=1 \\ |x+3|=(6)/(5) \\ x+3=(6)/(5),x+3=-(6)/(5) \\ x=(6)/(5)-3,x=-(6)/(5)-3 \\ x=1.2-3,x=-1.2-3 \\ x=-1.8,x=-4.2 \end{gathered}`

Hence the intercepts are (-1.8,0) and (-4.2,0).