Algebra 2 / Unit 2: Quadratic Functions and Complex Numbers
2.2 Solving Quadratic Equations
Notes
Set the equation equal to 0 (or isolate the square), then pick a method.
- Factoring: $x^2 - x - 12 = 0 \Rightarrow (x - 4)(x + 3) = 0 \Rightarrow x = 4$ or $x = -3$.
- Square roots: $(x - 1)^2 = 9 \Rightarrow x - 1 = \pm 3 \Rightarrow x = 4$ or $x = -2$. Don't forget the $\pm$.
- Completing the square: add $\displaystyle \left(\frac{b}{2}\right)^2$ to both sides when $a = 1$.
- Quadratic formula (always works):
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
Practice
Solve $x^2 - 5x - 14 = 0$.
$(x - 7)(x + 2) = 0$.
Solve $(x - 3)^2 = 25$.
$x - 3 = \pm 5$, so $x = 3 + 5$ or $x = 3 - 5$.
Solve $2x^2 + 3x - 1 = 0$.
$b^2 - 4ac = 9 - 4(2)(-1) = 17$ and $2a = 4$.
Ready for more? Take the Unit 2 test.