16.1: Math Talk: When $x$ Is -7
Evaluate each expression when \(x\) is -7:
16.2: Four Functions
- Complete the table of values for each function.
\(x\) 0 1 2 3 4 5 6 7 \(f(x)\)
\(x\) 0 1 2 3 4 5 6 7 \(g(x)\)
- Use the completed tables to answer these questions:
- What are the coordinates of the vertex of each graph? How can you tell?
- Does the graph of function \(f\) open up or down? How can you tell?
- Does the graph of function \(g\) open up or down? How can you tell?
- 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.
- What are the coordinates of the vertex of the graph of \(h\) and \(j\)?
- 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.
- Make a rough sketch of a graph of each function. Label the vertex of each graph with its coordinates.
- Here are some expressions that define quadratic functions. Match each function \(t\), \(u\), \(v\), and \(w\) with an expression that defines it.
- \(3x^2 + 1\)
- \(3(x-4)^2 + 1\)
- \(\text-3x^2 + 1\)