8.0k views
5 votes
A student wants to graph the function f(x) = -x^3 - 4x^2 + 9x + 36. Which characteristics will help the student graph the function correctly?

User Farris
by
8.2k points

1 Answer

3 votes

Final answer:

To graph the function f(x) = -x^3 - 4x^2 + 9x + 36 accurately, the student should consider identifying the x-intercepts, y-intercept, vertex, and end behavior of the graph.

Step-by-step explanation:

In order to graph the function f(x) = -x^3 - 4x^2 + 9x + 36 accurately, there are several characteristics that can be helpful:

  1. Identifying the x-intercepts: The x-intercepts are the points where the graph crosses the x-axis. To find them, set f(x) equal to zero and solve the resulting equation.
  2. Identifying the y-intercept: The y-intercept is the point where the graph crosses the y-axis. To find it, substitute x = 0 into the equation and evaluate f(0).
  3. Finding the vertex: The vertex is the minimum or maximum point of the graph. To find it, first find the x-coordinate of the vertex using the formula x = -b/2a, where the equation is in the form ax^2 + bx + c. Then substitute the x-coordinate back into the equation to find the corresponding y-coordinate.
  4. Determining the end behavior: Look at the signs of the leading coefficient and the highest power of x to determine the behavior of the graph as x approaches positive and negative infinity.

User ChrisPhoenix
by
9.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.