Friday Warm Up!

Evaluate for the given values:

1. 3, 4, 8 2. 11, 5, 7a b c a b c

80 283

3. Sketch the graph for each quadratic

No solutions One solution Two solutions

Using the Discriminant

I can use the discriminant to determine how many solutions a quadratic equation will have.

Discriminant: The expression under the radical in the quadratic formula that allows you to determine how many solutions you will have before solving it.

Using the Discriminant

2

2

4ab

a

bx

c

Quadratic Equations can have two, one, or no solutions.

Discriminant

Properties of the Discriminant

2 4 0b ac 2 Real Solutions

2 4 0b ac 1 Real Solution

2 4 0b ac No Real Solutions2 Imaginary Solutions

Discriminant is a positive number

Discriminant is zero

Discriminant is a negative number

*If the discriminant is a perfect square, the two real solutions are rational. *If the discriminant is not a perfect square, the two real solutions are irrational

2) 3 5 1a x x Ex. 1 Find the number of solutions of the following.

23 5 1 0x x 5

1

3

c

b

a

2 (3( 5 )4 )) ( 1

25 1237 0

2 solutions

2.) 2 3b x x

2

3

1

c

b

a

2 4(1( 2) 3))(

2 2 3 0x x

4 128

NO solutions

0

2.) 4 4 1c x x

4

1

4

c

b

a

2 4(4( 4) 1))(

24 4 1 0x x

16 160

1solution

0