Lesson 12

Evaluate each expression when \(x\) is -5:

\(\text-2x\)

\(x^2\)

\(\text-2x^2\)

\(\text-x^2\)

1. Two students are evaluating \(x^2+7\) when \(x\) is -3. Here is their work. Do you agree with either of them? Explain your reasoning. 

   Tyler:

   \(x^2+7\)

   \(\text-3^2+7\)

   \(\text-9+7\)

   -2

   Lin:

   \(x^2+7\)

   \((\text-3)^2+7\)

   \(9+7\)

   16

2. Evaluate each expression when \(x\) is -4:

   1. \(x^2\)
   2. \(\frac12 x^2\)
   3. \(\text-\frac18 x^2\)
   4. \(\text-x^2-8\)

3. Using graphing technology, graph \(y = x\). Then, experiment with the following changes to the function. Record your observations (include sketches, if helpful).

   1. Adding different constant terms to \(x\) (for example: \(x + 4\), \(x - 3\)).
   2. Multiplying \(x\) by different positive coefficients greater than 1 (for example: \(6x, 2.5x\)).
   3. Multiplying \(x\) by different positive coefficients between 0 and 1 (for example: \(0.25x, 0.1x\)).
   4. Multiplying \(x\) by negative coefficients (for example: \(\text-9x, \text-4x\)).

4. Use your observations to sketch these functions on the coordinate plane, which currently shows \(y=x\). 

   1. \(y =\text-0.5x + 2.1\)

   2. \(y = 2.1x - 0.5\)

      

      

      

      

1. Evaluate each expression when \(x\) is -3.
   1. \(x^2\)
   2. \(\text-x^2\)
   3. \(x^2+20\)
   4. \(\text-x^2+20\)
2. For each graph, come up with an equation that the graph could represent. Verify your equation using graphing technology.