Lesson 13

• Let’s explore the constants in Quadratic Equations

13.1: Math Talk: Halved and Squared

For each value of $$b$$, mentally find $$\left(\frac{b}{2} \right)^2$$.

$$b = 6$$

$$b = \frac{1}{2}$$

$$b = \frac{2}{5}$$

$$b = 0.8$$

13.2: Solving Quadratics with Perfect Squares

Solve each of these equations for all values of $$x$$ that make the equation true.

1. $$(x+2)^2 = 9$$
2. $$(x-\frac{1}{2})^2 = 4$$
3. $$(x+1)^2 = 8 + 1$$
4. $$(x-\frac{1}{3})^2 = \frac{10}{9}- \frac{1}{9}$$
5. $$(x-6)(x-6) = 81$$

13.3: Make It a Perfect Square

For each expression:

• Find a value that could be added as a constant term to make each expression a perfect square.
• Add the value you found and rewrite the expression in factored form.
1. $$x^2 + 20x$$
2. $$x^2 - 4x$$
3. $$x^2 - 2x$$
4. $$x^2 + x$$
5. $$x^2 + 5x$$
6. $$x^2 + 1.4x$$