IM Alg1.6.11 Lesson: Graphing from the Factored Form
Here is a graph of a function defined by . Three points on the graph are labeled.
Find the values of , , , , , and . Be prepared to explain your reasoning.
Consider two functions defined by and .
Complete the table of values for each function. Then, determine the -intercepts and vertex of each graph. Be prepared to explain how you know.
-intercepts:
Vertex:
-intercepts:
Vertex:
Plot the points from the tables on the same coordinate plane. (Consider using different colors or markings for each set of points so you can tell them apart.)
Make a couple of observations about how the two graphs compare.
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.
Sketch a graph that represents the expression and that shows the -intercepts and the vertex. Think about how to find the -coordinate of the vertex. Be prepared to explain your reasoning.
The quadratic function is given by . Find and .
What is the -coordinate of the vertex of the graph of this quadratic function?
Does the graph have any -intercepts? Explain or show how you know.