Question

I just need help figuring out this graph

Answer 1

y = | x - 2 | + 2

Explanation:

the equation of the absolute value function in standard form is

y = a | x - h | + k

(h, k ) are the coordinates of the vertex and a the vertical stretch

here vertex = (2, 2 ) with h = 2, k = 2 and a = 1 , then

y = | x - 2 | + 2 ← equation of graph

Answer 2

`y=|x-2|+2`

Explanation:

The general equation of an absolute value function is:

`\boxed{\begin{array}{l}\underline{\textsf{Absolute Value Function}} \\\\\Large\textx-h\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$(h,k)$ is the vertex.}\\\phantom{ww}\bullet\;\textsf{$a$ is the leading coefficient.}\end{array}}`

If a > 0, the V-shaped graph opens upwards.

If a < 0, the V-shaped graph opens downwards.

The provided graph shows the graph of an absolute value function that opens upwards with its vertex at (2, 2). Therefore:

• 
  `h = 2`
• 
  `k = 2`

Substitute the vertex into the equation:

`y=a|x-2|+2`

To find the value of the leading coefficient (a), substitute a point on the graph into the equation and solve for a:

`\begin{aligned}\textsf{Point}\;(0,4)\implies a|0-2|+2&=4\\a|-2|&=2\\2a&=2\\a&=1\end{aligned}`

Substituting the value of a into the equation gives:

`y=(1)|x-2|+2`

`y=|x-2|+2`

Therefore, the equation for the provided graph is:

`\Large\boxed{\boxedx-2}`