- This graph has two x-intercepts: x = -1 and 2.
- The y-intercept: y = 2.
- At x = 2 the graph passes through the axis linearly, suggesting the corresponding factors of the polynomial will be linear.
- At x = -1, the graph bounces off the x-axis at the intercept suggesting the corresponding factor of the polynomial will be second degree (quadratic).
Therefore, this gives us:
[tex]f(x)=a(x+1)^2(x-2)[/tex]
To determine the stretch factor (a), we utilize another point on the graph. We will use the y-intercept (0, 2), to solve for a:
[tex]\begin{gathered} f(0)=a(0+1)^2(0-2) \\ 2=a(1)^2(-2) \\ 2=-2a \\ \frac{2}{-2}=\frac{-2a}{-2} \\ a=-1 \end{gathered}[/tex]
The graphed polynomial appears to represent the function:
[tex]f(x)=-1(x+1)^2(x-2)[/tex]
Answer:
[tex]f(x)=-1(x-2)(x+1)^2[/tex]
