Using the Quadratic Formula

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1. 1. The problem0:00
   Using the Quadratic Formula

   $2x^2 + 3x - 2 = 0$
2. 2. The formula0:11
   $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

   for $ax^2 + bx + c = 0$

3. 3. The discriminant0:29
   1. $$b^2 - 4ac = 3^2 - 4(2)(-2)$$
   2. $$= 9 + 16 = 25$$
      positive, so two real roots
   3. $$\sqrt{25} = 5$$
4. 4. Both roots0:48
   1. $$x = \frac{-3 \pm 5}{4}$$
   2. $$x = \frac{-3 + 5}{4} = \frac{2}{4} = \frac{1}{2}$$
   3. $$x = \frac{-3 - 5}{4} = \frac{-8}{4} = -2$$
5. 5. See it on the graph1:03

6. 6. Recap1:10
   • ✓Write the equation as $ax^2 + bx + c = 0$.
   • ✓Compute $b^2 - 4ac$ first: it tells you how many real roots.
   • ✓Simplify each sign separately.

Solve by factoring, completing the square or the quadratic formula; use the discriminant.

• Quadratic Equation Calculator: try the same kind of problem with your own numbers.
• Complete the Square Calculator: try the same kind of problem with your own numbers.
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• Quadratic Equations Study Guide (study guide)
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