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.
 \(a=k^2\)
 \(b=2k\boldcdot m\)
 \(c=m^2\)
 \(k = 1, m = 3\)
 \(k=2, m= 3\)
 \(k=2, m=4\)
 \(k = 3, m = 5\)
14.2: Practice Writing Expressions in Standard Form
In their math class, Priya and Tyler are asked to rewrite \((5x+2)(x3)\) into standard form.
Priya likes to use diagrams to rewrite expressions like these, so her work looks like this.
\(x\)  3  
\(5x\)  \(5x^2\)  \(\text15x\) 
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.
\(5x(x3) + 2(x3)\)
\(5x^2  15x + 2x  6\)
\(5x^2  13x  6\)
Use either of these methods or another method you prefer to rewrite these expressions into standard form.
 \((2x+1)(2x3)\)
 \((4x  1)(\frac{1}{2}x  3)\)
 \((3x5)^2\)
 \((2x+1)^2\)
14.3: Find the Values
For each question, find the value of \(k\) and \(m\) then determine the value of \(m^2\).

 \(k > 0\)
 \(k^2 = 100\)
 \(2km = 40\)

 \(k < 0\)
 \(k^2 = 9\)
 \(2km = 30\)

 \(k < 0\)
 \(k^2 = 16\)
 \(2km = \text{}40\)

 \(k > 0\)
 \(k^2 = 4\)
 \(2km = \text{}28\)

 \(k > 0\)
 \(k^2 = 49\)
 \(2km = 14\)

 \(k > 0\)
 \(k^2 = 0.25\)
 \(2km = 12\)