1. Find the x coordinate using -b/2a, then find the y coordinate.
1.) y = x2 + 4x - 2
2.) y = 2x2 - 4x - 4

2. y = 4 - 8 - 2 y = -6 Vertex = (-2,-6) 1.) y = x2 + 4x - 2

3. 2.) y = 2x2 - 4x - 4 y = 2 - 4 - 4 y = -6 Vertex = (1,-6)

4. Today’s Objective
To be able to solve a quadratic equation by using the quadratic formula.

5. Solving Equations with a radical
Solve for x
x2 = 81
x = 81
x =  9
Review

6. Solving Equations with a radical
Solve for x
x2 = 5
x = 5
x =  5
Review

7. The Quadratic Formula ax2 + bx + c = 0 x = -b b2 - 4ac 2a
For equations of the form
ax2 + bx + c = 0
x = -b b2 - 4ac a

8. Minus b, plus or minus the square root of b2 minus 4ac divided by 2a
The Quadratic Formula
Minus b, plus or minus the square root of b2 minus 4ac divided by 2a

9. The Quadratic Formula
x = -b b2 - 4ac a

10. The Quadratic Formula
y = ax2 +bx + c
x2 -3x -18 = 0
x = -b b2 - 4ac a
x = (-3)2 - 4•1•(-18) •1

11. The Quadratic Formula
x = (-3)2 - 4•1•(-18) •1
x = =
x =3 + 9 =
x =3 - 9 =

12. So The Solution is:::
x2 -3x -18 = 0
x = 6 and -3

13. The Quadratic Formula
y = ax2 +bx + c
x2 - 9x + 18=0
x = -b b2 - 4ac 2a
x = (-9)2 - 4•1•18
2•1

14. The Quadratic Formula
x = (-9)2 - 4•1•18
2•1
x = =9+ 9
x =9 + 3 =
x =9 - 3 =

15. So The Solution is:::
x2 -9x +18 = 0
x = 6 and 3

16. Now You Try First replace a,b,c in the formula
x2 +3x -18 = 0
x = -b b2 - 4ac a

17. Now You Try First replace a,b,c in the formula
x2 +3x -18 = 0
x = •1•(-18) •1

18. Now solve the formula
x = •1•(-18) •1
x =

19. Now solve the formula
x =
x =
x = 3, -6

20. Classwork
Worksheet 9.4
Extra Practice (1-6)
Homework page 475 (7-17)