The equation of a parabola in factored form is:
[tex]y=a(x-x_1)(x-x_2)[/tex]where a is the leading coefficient, and x1 and x2 are the zeros of the parabola.
From the graph, we can see that the zeros (the x-intercepts) are x1 = -1 and x2 = 4. We also know that when x = 0, y = -1 (from the y-intercept), replacing this information into the above equation, we get:
[tex]\begin{gathered} -1=a\cdot(0-(-1))\cdot(0-4) \\ -1=a\cdot1\cdot(-4) \\ -1=a\cdot(-4) \\ \frac{-1}{-4}=a \\ \frac{1}{4}=a \end{gathered}[/tex]Finally, the equation of the parabola is:
[tex]\begin{gathered} y=\frac{1}{4}(x-(-1))(x-4) \\ y=\frac{1}{4}(x+1)(x-4) \end{gathered}[/tex]