# Lesson 13

Constants in Quadratic Equations

- 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.

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

### 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.

- \(x^2 + 20x\)
- \(x^2 - 4x\)
- \(x^2 - 2x\)
- \(x^2 + x\)
- \(x^2 + 5x\)
- \(x^2 + 1.4x\)