SOLUTION: Hello, I am trying to figure out how to graph this following equation. y=(x-2)^2(x+5) and include the domain and range. Thanks in advance

Algebra ->  Graphs -> SOLUTION: Hello, I am trying to figure out how to graph this following equation. y=(x-2)^2(x+5) and include the domain and range. Thanks in advance      Log On


   

Question 895052: Hello, I am trying to figure out how to graph this following equation.
y=(x-2)^2(x+5) and include the domain and range. Thanks in advance
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
This equation being in factored form is convenient.
ZEROS: x=2 and x=-5.
DEGREE is 3.
Leading term: 1%2Ax%5E3

Those facts tell you where the graph crosses the x-axis, and indicates that y decreases toward the left of x=-5, and increases toward the right of x=2 as x increases. Domain & Range, all real numbers.
You can check signs in the intervals which the critical values of x form, just to be more clear of the shape before you try to sketch the graph. Note the (x-2)^2, so the factor occurs with multiplicity of two.

graph%28300%2C300%2C-20%2C20%2C-25%2C25%2C%28x-2%29%5E2%28x%2B5%29%29

graph%28300%2C300%2C-12%2C12%2C-10%2C55%2C%28x-2%29%5E2%28x%2B5%29%29