Answer:
From the graph, the roots of the equation are given below as
[tex]\begin{gathered} x=-3 \\ x=1 \end{gathered}[/tex]
These are the points where the curve cuts the x-axis
The y-intercepts of the graph is given below as
[tex](0,-3)[/tex]
Concept:
To find the equation of the graph, we will use the formula below
[tex]\begin{gathered} f(x)=a(x+3)(x-1) \\ x=0,y=-3 \\ -3=a(0+3)(0-1) \\ \frac{-3}{-3}=\frac{-3a}{-3} \\ a=1 \end{gathered}[/tex]
Hence,
By substituting the values, we will have
[tex]\begin{gathered} f(x)=a(x+3)(x-1) \\ f(x)=1(x+3)(x-1) \\ f(x)=x^2-x+3x-3 \\ f(x)=x^2+2x-3 \end{gathered}[/tex]
Hence,
The function of the graph is
[tex]f(x)=x^2+2x-3[/tex]
OPTION D is the right answer
