5.5 – The Quadratic formula

Objectives: Use the quadratic formula to find real roots of quadratic equations.

Use the roots of a quadratic equation to locate the axis of symmetry of a parabola.

Standard: 2.8.11.N. Solve quadratic equations.

a = -1 b = -3 c = 8 a = 4 b = 2 c = -3

a = -4 b = -5 c = -5 a = 1 b = -6 c = 7

• QUADRATIC FORMULA:• If ax2+ bx + c = 0 and a ≠ 0, then the

solutions, or roots, are

aacbbx

242

Use the quadratic formula to find the roots. Give exact solutions & approximate solutions to the nearest tenth.

Example 1a.x2 – 7x + 6 = 0a = 1, b = -7, c = 6

or

or

)1(2)6)(1(4)7()7( 2

x

224497

x

2257

x

257

x

257

x2

57 x

212

x

6x

22

x

1x

Example 1b

4x2 = 8 – 3x0 = -4x2 + 8 – 3xa = -4, b = -3, c = 8

or

)4(2)8)(4(4)3()3( 2

x

812893

x

81373

x8

1373x

81373or

81373

xx

84.1or 09.1 xx

Example 1c

2x2 – 6x = -32x2 – 6x + 3 = 0a = 2, b = -6, c = 3

)2(2)3)(2(4)6()6( 2

x

424366

x

4126

x

4126or

4126

xx

4126or

4126

xx

63.0or 37.2 xx

Example 2After watching a home-improvement show, the Wilkersons decided to

build a patio along two sides of their home.Find the width of the patio if there is enough material to cover a

surface area of 650 square feet. 2( ) 25 30A x x x x 2 55x x

2

Solve this equation:

55 650x x

2 55 650 0x x

255 55 4(1)( 650)2(1)

x

55 752

x

10 or 65x x Non

sense

Example 4a2( ) 4 1f x x x

Example 4b2( ) 7 6 5f x x x

Example 4c2( ) 9 14f x x x

Example 4d2( ) 2 2f x x x

Homework

Packet section 5.5