SOLUTION: Use the following information to graph the polynomial on graph paper f(x) = 3(x+4)(x-5)^2 a) Use tle leading coefficient test to determine the graph end's behavior b) Find the

Algebra ->  Equations -> SOLUTION: Use the following information to graph the polynomial on graph paper f(x) = 3(x+4)(x-5)^2 a) Use tle leading coefficient test to determine the graph end's behavior b) Find the      Log On


   

Question 377706: Use the following information to graph the polynomial on graph paper
f(x) = 3(x+4)(x-5)^2
a) Use tle leading coefficient test to determine the graph end's behavior
b) Find the x-intercepts, State whether the graph crosses the x-axis or touches the x-axis and turns around
zero multiplicity cross/touch
c) find the y-intercept
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a) The leading term of the polynomial if the factors were multiplied out is 3x%5E3. Thus as x approaches -infinity, f(x) goes to -infinity. Similarly, as x approaches infinity, f(x) goes to infinity.
b) The x-intercepts correspond to the roots -4 and 5. -4 is a single root, and so it has to cross the x-axis (from - to +). 5 is a double root ( or multiplicity 2), and so it turns and touches the x-axis (it stays on or ABOVE the x-axis).
c) When x = 0, f%280%29+=+3%2A%280%2B4%29%2A%280-5%29%5E2+=+3%2A4%2A25+=+300. That is the y-intercept.