Lesson 4

Evaluating Quadratic and Exponential Functions

  • Let’s work fluently with exponents.

4.1: Math Talk: Exponents

Evaluate mentally.

\(4^2\)

\(2^4\)

\(2^6\)

\(4^3\)

4.2: Evaluating and Describing Functions

  1. Different students are evaluating two expressions, \(3\boldcdot 6^x\) and \(5^x\). Analyze their work, describe any errors made, and then evaluate each expression correctly.

      Noah’s work Mai’s work  corrected work  
    Evaluate \(5^x\) when \(x\) is 6.

    \(5^x\)

    \(5^6\)

    30

    \(5^x\)

    \(5^6\)

    \(6 \boldcdot 6 \boldcdot 6 \boldcdot 6 \boldcdot6\)

    7,776

     
    Evaluate \(3 \boldcdot 6^x\) when \(x\) is 2.

    \(3 \boldcdot 6^x\)

    \(3\boldcdot 6^2\)

    \(3 \boldcdot 12\)

    36

    \(3 \boldcdot 6^x\)

    \(3 \boldcdot 6^2\)

    \(18^2\)

    324

     
  2. Here are three functions. For each function:
    1. Complete the table of values.
    2. Sketch a graph.
    3. Decide whether each function is linear, quadratic, or exponential, and be prepared to explain how you know.

    \(f(x)=3 \boldcdot 2^x\)

    \(x\) -1 0 1 2 3 5
    \(f(x)\)            

     

    horizontal axis, scale 0 to 5, by 1's. vertical axis, scale 0 to 110, by 10's.

    \(g(x)=3 \boldcdot x^2\)

    \(x\) -1 0 1 2 3 5
    \(g(x)\)            

     

    horizontal axis, scale 0 to 5, by 1's. vertical axis, scale 0 to 110, by 10's.

    \(h(x)=3 \boldcdot 2x\)

    \(x\) -1 0 1 2 3 5
    \(h(x)\)            

     

    horizontal axis, scale 0 to 5, by 1's. vertical axis, scale 0 to 110, by 10's.

4.3: Evaluating Exponential and Quadratic Expressions

For each row, you and your partner will each evaluate an expression. You should each get the same answer in each row. If you disagree, work to reach agreement.

row Partner A PartnerB
1 \(4 \boldcdot 2^x\) when \(x\) is 3 \(2 \boldcdot 2^x\) when \(x\) is 4
2 \(19 + x^2\) when \(x\) is 9 \(4 \boldcdot x^2\) when \(x\) is 5
3 \(16 \boldcdot 2^x\) when \(x\) is 0 \(2 \boldcdot 2^x\) when \(x\) is 3
4 \(\frac12 \boldcdot 2^x\) when \(x\) is 4 \(x^2-1\) when \(x\) is 3
5 \(x^2+1\) when \(x\) is 7 \(18+2^x\) when \(x\) is 5
6 \(4+2^x\) when \(x\) is 4 \(\frac15 x^2\) when \(x\) is 10
7 \(0.1 x^2\) when \(x\) is 6 \(0.4 x^2\) when \(x\) is 3
8 \(45 \boldcdot x^2\) when \(x\) is \(\frac13\) \(10 \boldcdot 2^x\) when \(x\) is -1
9 \(x^2\) when \(x\) is -4 \(64x^2\) when \(x\) is \(\frac12\)
10 \(\text-2 x^2\) when \(x\) is 3 \(\text-2 x^2\) when \(x\) is -3

 

Summary