IM Alg1.6.15 Lesson: Vertex Form
What do you notice? What do you wonder?
Set 1: Set 2:
Here are two sets of equations for quadratic functions you saw earlier.
In each set, the expressions that define the output are equivalent.
The expression that defines is written in vertex form. We can show that it is equivalent to the expression defining by expanding the expression:
Show that the expressions defining and are equivalent.Set 1: Set 2:
Here are graphs representing the quadratic functions.
Why do you think expressions such as those defining and are said to be written in vertex form?
Graph of Graph of
Using graphing technology, graph y=x².
Then, add different numbers to before it is squared (for example, , ) and observe how the graph changes. Record your observations.
Graph . Then, experiment with each of the following changes to the function and see how they affect the graph and the vertex:
Without graphing, predict the coordinates of the vertex of the graphs of these quadratic functions, and predict whether the graph opens up or opens down. Ignore the last row until the next question.
Use graphing technology to check your predictions. If they are incorrect, revise them. Then, complete the last row of the table.
What is the vertex of this graph?
Find a quadratic equation whose graph has the same vertex and adjust it, if needed, so that it has the graph provided.