5.6 Quadratic Formula & Discriminant

By: L. Keali’i Alicea

Goals

Solve quadratic equations using the quadratic formula.

Use the quadratic formula in real-life situations.

Discriminant: b2-4ac

The discriminant tells you how many solutions and what type you will have.

If the discrim: Is positive – 2 real solutions

Is negative – 2 imaginary

solutions

Is zero – 1 real solution

Examples Find the discriminant

and give the number and type of solutions.

a. 9x2+6x+1=0

a=9, b=6, c=1

b2-4ac=(6)2-4(9)(1)

=36-36=0

1 real solution

b. 9x2+6x-4=0

a=9, b=6, c=-4

b2-4ac=(6)2-4(9)(-4)

=36+144=180

2 real solutions

c. 9x2+6x+5=0

a=9, b=6, c=5

b2-4ac=(6)2-4(9)(5)

=36-180=-144

2 imaginary solutions

Quadratic Formula(Yes, it’s the one with the song!)

If you take a quadratic equation in standard form (ax2+bx+c=0), and you complete the square, you will get the quadratic formula!

a

acbbx

2

42

When to use the Quadratic Formula

Use the quadratic formula when you can’t factor to solve a

quadratic equation. (or when you’re stuck on how to

factor the equation.)

Examples1. 3x2+8x=35

3x2+8x-35=0

a=3, b=8, c= -35

6

420648 x

)3(2

)35)(3(4)8()8( 2 x

6

4848x

6

228x

3

7

6

14

6

228

x

OR

56

30

6

228

x

2. -2x2=-2x+3

-2x2+2x-3=0

a=-2, b=2, c= -3

)2(2

)3)(2(4)2()2( 2

x

4

2442

x

4

202

x

4

5*4*12

x

4

522

i

x

4

52

4

2

i

x

2

5

2

1 ix

Assignment

5.6 A (odd)