# Lesson 16

Graphing from the Vertex Form

• Let’s use vertex form to reason about a graph.

### 16.1: Math Talk: When $x$ Is -7

Evaluate each expression when $$x$$ is -7:

$$x+4$$

$$(x+4)^2$$

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

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

### 16.2: Four Functions

1. Complete the table of values for each function.

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

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

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

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

### 16.3: Four More Functions

Here are some tables of values that represent quadratic functions.

 $$x$$ $$t(x)$$ 2 3 4 5 6 7 8 -11 -2 1 -2 -11 -26 -47
 $$x$$ $$u(x)$$ -2 -1 0 1 2 3 4 13 4 1 4 13 28 49
 $$x$$ $$v(x)$$ -1 0 1 2 3 4 5 76 49 28 13 4 1 4
 $$x$$ $$w(x)$$ -4 -3 -2 -1 0 1 2 -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. $$\text-3x^2 + 1$$