Answer:
The graph is attached.
Step-by-step explanation:
This function is in factored form,
f(x) = (x-r₁)(x-r₂), where r₁ and r₂ are the roots of the function. This means the roots, or x-intercepts, of this function are at x = -3 and x = 2.
Next we find the vertex. We start by finding the axis of symmetry; in factored form, this is given by
[tex]x=\frac{r_1+r_1}{2}[/tex]
For our function, we have
x = (-3+2)/2 = -1/2 = -0.5.
We plug this into the function to find the y-coordinate of the vertex:
f(-0.5) = (-0.5+3)(-0.5-2) = 2.5(-2.5) = -6.25
This makes the vertex (-0.5, -6.25).
We plot this vertex; then we plot the roots and draw the parabola through the three points.
