Cool Down
1. Consider the quadratic equation . Consider the graph of the equation when answering questions a and b.
a. Where are the -intercepts located?
Compare your answer:
The -intercepts are at and .
b. What is the -coordinate of the vertex?
2. The vertex is halfway between the intercepts at .
2. Here is a graph of .
Sketch this graph, then sketch a graph of on the same graph. Briefly explain how you know where to sketch the graph.
Compare your answer:
is equivalent to , so the -intercepts are at and . Calculate the vertex by finding the -coordinate in between and which is . Substitute into the equation to find the -coordinate: . The vertex is at . The squared term has a positive coefficient so the graph opens upward. Adding a positive linear term to shifts the graph down and to the left.