# Lesson 14

• 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 $$m^2$$.

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