Lesson 16

Evaluate each expression when \(x\) is -7:

\(x+4\)

\((x+4)^2\)

\(\text-(x+4)^2\)

\(\text-(x+4)^2+5\)

1. Complete the table of values for each function.

   \(f(x)=(x-4)^2\)

   \(x\)	0	1	2	3	4	5	6	7
   \(f(x)\)

   \(g(x)=\text-(x-4)^2\)

   \(x\)	0	1	2	3	4	5	6	7
   \(g(x)\)

2. Use the completed tables to answer these questions:
   1. What are the coordinates of the vertex of each graph? How can you tell?
   2. Does the graph of function \(f\) open up or down? How can you tell?
   3. Does the graph of function \(g\) open up or down? How can you tell?
3. Suppose function \(h\) is defined by \(h(x) = (x-4)^2 + 5\) and function \(j\) is defined by \(j(x) = \text-(x-4)^2 + 5\). Make predictions about the graph of each function using the questions here. If you get stuck, try creating a tables of values.
   1. What are the coordinates of the vertex of the graph of \(h\) and \(j\)?
   2. Which way—up or down—does the graph of each function open? How do you know?

Here are some tables of values that represent quadratic functions.

\(x\)	2	3	4	5	6	7	8
\(t(x)\)	-11	-2	1	-2	-11	-26	-47

\(x\)	-2	-1	0	1	2	3	4
\(u(x)\)	13	4	1	4	13	28	49

\(x\)	-1	0	1	2	3	4	5
\(v(x)\)	76	49	28	13	4	1	4

\(x\)	-4	-3	-2	-1	0	1	2
\(w(x)\)	-47	-26	-11	-2	1	-2	-11

1. Make a rough sketch of a graph of each function. Label the vertex of each graph with its coordinates.
    

   

   

   

   

   

   

   

   

   
    
2. Here are some expressions that define quadratic functions. Match each function \(t\), \(u\), \(v\), and \(w\) with an expression that defines it. 
   1. \(3x^2 + 1\)
   2. \(\text-3(x-4)^2+1\)
   3. \(3(x-4)^2 + 1\)
   4. \(\text-3x^2 + 1\)