The Quadratic Formula

The Quadratic Formula

The Quadratic Formula There are multiple ways to solve a quadratic equation.

ax  bx  c  0 2

Using a method called the quadratic formula, any quadratic equation can be solved.

The Quadratic Formula Quadratic Equation

ax  bx  c  0 2

Quadratic Formula

– b  b – 4ac x 2a 2

We can solve a quadratic equation by substituting the corresponding a, b, and c values into the formula.

The Quadratic Formula

ax  bx  c  0 2

2 x  8 x – 24  0 2

a 2

b 8

c  – 24

– b  b – 4ac x 2a 2

The Quadratic Formula

a 2

b 8

c  – 24

– b  b – 4ac x 2a 2

– b  b – 4ac x 2a 2

The Quadratic Formula

a 2

b 8

c  – 24

– b  b – 4ac x 2a 2

– b  b – 4(2)c x 2(2) 2

The Quadratic Formula

a 2

c  – 24

b 8

– b  b – 4ac x 2a 2

– (8)  (8) – 4(2)c x 2(2) 2

The Quadratic Formula

a 2

b 8

c  – 24

– b  b – 4ac x 2a 2

– (8)  (8) – 4(2)(–24) x 2(2) 2

The Quadratic Formula – b  b 2 – 4ac x 2a

– (8)  (8) – 4(2)(–24) x 2(2) 2

– (8)  64 – (–192) x 4 – (8)  256 x 4

a2 b 8 c  – 24 – 8  16 x 4

x  –2  4 x  –2  4

x  –2 – 4

x2

x  –6

The Quadratic Formula Checking Solutions

x2

x  –6

2 x  8 x – 24  0

2 x  8 x – 24  0

2(2)  8(2) – 24  0

2(–6)  8(–6) – 24  0

2(4)  16 – 24  0

2(36)  (–48) – 24  0

8  16 – 24  0 00

72  (–48) – 24  0 00

2

2

2

2

The Quadratic Formula The quadratic formula reveals information about the roots of the quadratic equations.

Quadratic Formula b2 – 4ac > 0, = a Perfect Square

Roots

Real? Rational? Equal?

b2 – 4ac > 0, ≠ a Perfect Square

b2 – 4ac =0

b2 – 4ac