Answer: Local Max = (-1, 0)
Local Min = (1, -8)
<u>Step-by-step explanation:</u>
f(x) = (x + 1)² (x - 3)
<u />
<u>Step 1:</u> Find the zeros
(x + 1)² = 0 --> x = -1 <em> (multiplicity of 2)</em>
(x - 3) = 0 --> x = 3
<u>Step 2:</u> Find the Vertices
x = -1 --> (multiplicity is even which means this is a vertex)
The midpoint between x = -1 and x = 3 is x = 1
<u>Step 3:</u> Find the Local Max and Local Min
Use the x-value above to find the y-values
f(-1) = 0 <em>because it is a zero</em>
f(1) = (1 + 1)² (1 - 3)
= 2²(-2)
= 4(-2)
= -8
<u>Conclusion:</u>
(-1, 0) is the Local Max bigger y-value
(1, -8) is the Local Min smaller y-value