Lesson 14

Rewriting Quadratic Expressions

  • Let’s practice rewriting quadratic expressions

14.1: Writing Quadratics in Standard Form

Use the given information to write a quadratic expression in standard form.

  • \(a=k^2\)
  • \(b=2k\boldcdot m\)
  • \(c=m^2\)
  1. \(k = 1, m = 3\)
  2. \(k=2, m= 3\)
  3. \(k=2, m=4\)
  4. \(k = 3, m = 5\)

14.2: Practice Writing Expressions in Standard Form

In their math class, Priya and Tyler are asked to rewrite \((5x+2)(x-3)\) into standard form.

Priya likes to use diagrams to rewrite expressions like these, so her work looks like this. 

\(x\) -3
\(5x\) \(5x^2\) \(\text-15x\)
2 \(2x\) -6

\(5x^2 - 15x + 2x - 6\)

\(5x^2 -13x - 6\)

Tyler likes to use the distributive property to rewrite expressions like these, so his work looks like this.

\(5x(x-3) + 2(x-3)\)

\(5x^2 - 15x + 2x - 6\)

\(5x^2 - 13x - 6\)

Use either of these methods or another method you prefer to rewrite these expressions into standard form.

  1. \((2x+1)(2x-3)\)
  2. \((4x - 1)(\frac{1}{2}x - 3)\)
  3. \((3x-5)^2\)
  4. \((2x+1)^2\)

14.3: Find the Values

For each question, find the value of \(k\) and \(m\) then determine the value of \(m^2\).

    • \(k > 0\)
    • \(k^2 = 100\)
    • \(2km = 40\)
    • \(k < 0\)
    • \(k^2 = 9\)
    • \(2km = 30\)
    • \(k < 0\)
    • \(k^2 = 16\)
    • \(2km = \text{-}40\)
    • \(k > 0\)
    • \(k^2 = 4\)
    • \(2km = \text{-}28\)
    • \(k > 0\)
    • \(k^2 = 49\)
    • \(2km = 14\)
    • \(k > 0\)
    • \(k^2 = 0.25\)
    • \(2km = 12\)

Summary