A.6.11.3 What Do We Need to Sketch a Graph?

The functions f, g, and h are given. Predict the x-intercepts and the x-coordinate of the vertex of each function.
Use graphing technology to graph the functions f, g, and h. Use the graphs to check your predictions.

Without using technology, sketch a graph that represents the equation y = (x - 7)(x + 11) and that shows the x-intercepts and the vertex. Think about how to find the y-coordinate of the vertex. Explain your reasoning.

A quadratic function is defined by k(x) = (x - 100)(x + 20). How would you explain to a friend who is absent today how to use the equation to:

  1. Find the zeros of the function?
  2. Find the x-intercepts of the graph?
  3. Find the x-coordinate of the vertex without graphing?
  4. Find the y-coordinate of the vertex without graphing?
  5. Find the y-intercept of the graph?