Answer:
[tex]g(x)\text{ = -}\frac{1}{4}(x+1)\placeholder{⬚}^2+1[/tex]
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:
[tex]y\text{ = a\lparen x-h\rparen}^2+k[/tex]
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:
[tex]y\text{ = a\lparen x+1\rparen}^2+1[/tex]
Lastly, we need to get the value of a
We can use the point (1,0)
Substituting this value:
[tex]\begin{gathered} 0\text{ = a\lparen1+1\rparen}^2\text{ + 1} \\ 0\text{ = 4a + 1} \\ 4a\text{ = -1} \\ a\text{ =- }\frac{1}{4} \end{gathered}[/tex]
Thus, we have the equation of the plotted graph as:
[tex]g(x)\text{ = -}\frac{1}{4}(x+1)\placeholder{⬚}^2+1[/tex]
