Lesson 16

Find the value of these expressions.

1. \(\sqrt{9}+2\)
2. \(\frac{\sqrt{16}}{2}\)
3. \((\sqrt{25})^2+6.2)\)
4. \((\frac{\sqrt{100}}{4} - \frac{\sqrt{64}}{2})\)
5. \(\sqrt{1+ 15}\)
6. \(\sqrt{4^2 + 3^2}\)

Rewrite the equation in standard form \(ax^2 + bx + c = 0\), then identify \(a, b,\) and \(c\). Then compute \(b^2 - 4ac\).

1. \(x^2 - 3x + 5 = 0\)
2. \(3x^2 - 4 + x = 0\)
3. \(\text{-}2x^2 + 5x = 11\)
4. \(3x^2 + 5x = 9 - 4x\)
5. \(\frac{2x^2}{3} + 6x -13 = 13\)
6. \(x^2 - 9 = 0\)
7. \(9+x-4x^2 = 1\)
8. \((x+2)(x-3) = 0\)

Solve each of these quadratic equations by either rewriting the expression in factored form or completing the square. Explain or show your reasoning for the method you choose to use.

1. \(x^2 - 3x - 4 = 0\)
2. \(x^2 + x = 6\)
3. \(x^2 + 6x + 7 = 5\)
4. \(x^2 +12 = 7x\)
5. \(x^2 + 3x - 5 = 0\)