1. Warm Up Using the quadratic formula find the zeros of the following:
1. x2 – 9x + 12 = 0
2. x2 + 4x – 16 = 0
3. 2x2 + 8x – 13 = 0

2. Answers Using the quadratic formula find the zeros of the following:
1. x2 – 9x + 12 = x = 7.37, x = 1.63
2. x2 + 4x – 16 = x = 2.47, x = -6.47
3. 2x2 + 8x – 13= 0 x = 1.24, x = -5.24

3. discriminant

4. Create a rough sketch of the following quadratic functions
Create a rough sketch of the following quadratic functions. How many times does each quadratic touch the x-axis?

5. The discriminant determines how many solutions a quadratic function will have.

6. If the discriminant is POSITIVE, there are 2 REAL solutions.
If the discriminant is ZERO, there is 1 REAL solution
If the discriminant is NEGATIVE, there are 2 IMAGINARY solutions.

7. Find the discriminant for each quadratic equation.

8. Given the following quadratics, use the discriminant to determine how many solutions it will have.
1. x2 – 6x + 11 = x2 + 5x = 12
3. 3x = x2 – 27 = 0
5. x2 + x + 1 = x2 + 4x -1 = 0

9. Given the following graphs of a quadratic function:
Determine the sign of the discriminant.
Determine whether the solutions are real or imaginary.