Question

The graph above is a transformation of the function x ^ 2 Write an equation for the function graphed aboveg(x)=

Answer 1

`g(x)\text{ = -}(1)/(4)(x+1)\placeholder{⬚}^2+1`

Step-by-step explanation:

Here, we want to write an equation for the graph shown

The graph of x^2 is an upward-facing graph

The graph we have shown below is a graph that has been reflected and shifted

To get the equation of the graph we need to write it in the vertex form

The vertex form is:

`y\text{ = a\lparen x-h\rparen}^2+k`

The vertex of the graph is at (h,k)

Looking at the given graph, we have the vertex at (-1,1)

Thus, we have the equation as:

`y\text{ = a\lparen x+1\rparen}^2+1`

Lastly, we need to get the value of a

We can use the point (1,0)

Substituting this value:

`\begin{gathered} 0\text{ = a\lparen1+1\rparen}^2\text{ + 1} \\ 0\text{ = 4a + 1} \\ 4a\text{ = -1} \\ a\text{ =- }(1)/(4) \end{gathered}`

Thus, we have the equation of the plotted graph as:

`g(x)\text{ = -}(1)/(4)(x+1)\placeholder{⬚}^2+1`