1. Solve quadratic equations using the: QUADRATIC FORMULA

2. You will learn 5 different ways to solve a quadratic equations.
Solve by graphing
Solve by factoring
Solve using square roots
Solve by completing the square
Solve by the quadratic formula

3. QUADRATIC FORMULA You mainly use the when you have a
trinomial equation
that you
cannot
factor!!

4. 2a Quadratic Formula: x = -b + √ b² - 4ac for ax² + bx + c = 0
PARENTHESIS!!!!!
Quadratic Formula:
x = -b + √ b² - 4ac 2a
for ax² + bx + c = 0
This is on your formula sheet.

5. Quadratic equations can have:
Two distinct solutions.
One distinct solution.
No real solutions.

6. In order to figure out how many solutions a problem has we will find the discriminant.
Aka – The number under the radical.
Discriminant :
b2 – 4ac

7. If the discriminant is…
Positive – 2 solutions
Because the square root of a positive number always has 2 answers.
Zero – One solution
Because the square root of 0 is 0 and only 0.
Negative – No solution
Because you cannot take the square root of a negative number.

8. There are no real solutions There are two real solutions
Find the number of solutions of each equation using the discriminant.
1) 3x2 – 2x + 2 = 0
2) 2x2 + 11x + 12 = 0
There are no real solutions
There are two real solutions

9. There is one real solution There are two real solutions
Find the number of solutions of each equation using the discriminant.
3) x2 + 8x + 16 = 0
4) x2 – 9x + 4 = 0
There is one real solution
There are two real solutions

10. Steps: Solve using the quadratic equation.
Get all the terms to one side of the equals sign.
The other side should equal zero.
Find: a, b, and c.
Plug in a, b, and c to the formula. USE PARENTHESIS!!!!!
Simplify piece by piece. If you plug in all at once you will make a mistake.

11. Solve each equation by using the quadratic formula.
5.) x² – 7x +3 = 0

12. Solve each equation by using the quadratic formula.
6.) 3x² + 2x –3 = 0

13. Solve each equation by using the quadratic formula.
7.) 14 = 12 – 5x – x2

14. Solve each equation by using the quadratic formula.8)
x2 + 4x = -1

15. Solve each equation by using the quadratic formula.9)

16. Solve each equation by using the quadratic formula.
10)