Lesson 4

Equations and Their Zeros

  • Let’s work with equations in standard and factored forms

4.1: Math Talk: Equations with Zero

Mentally find a value for \(a\) that will make the equation true.

\(4a = 0\)

\(3 \boldcdot 0 = 14a\)

\(0 \boldcdot a = 0\)

\(ab = 0\) with \(b \neq 0\)

4.2: Evaluating Quadratic Equations

  1. Evaluate each function for \(x = 6\).
    1. \(f(x)=(x+4)(x-6)\)
    2. \(g(x)=(x-6)(x+6)\)
    3. \(h(x)=x^2-6x\)
    4. \(j(x)=2(\frac{2}{3}x+8)(x-6)\)
    5. \(k(x)= 0.5x^2 - 3x\)
  2. What do these functions have in common?
  3. For each function, find another value of \(x\) that would give the same output as you found earlier.

4.3: Card Sort: Matching Equation Forms

Your teacher will give you a set of cards. Match each function in standard form with an equivalent function in factored form.