Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Aim: What is the quadratic formula and how do we use it?

Do Now:Solve by completing the square:

x2 + 2x – 12 = 0

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Solving Quadratics by Graphing

Find the zeros by graphing: x2 + 3x – 10 = 0

x = -5 x = 2

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Solving Quadratics by Factoring

Solve: x2 + 3x – 10 = 0

(x + 5)(x – 2) = 0

(x + 5) = 0 (x - 2) = 0x = -5 x = 2

Graph the equation y = x2 + 3x – 10 on calculator

x = -5 x = 2

the roots of the quadratic -where the parabola crossesthe x-axis.

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Solving Quadratics

Graph: x2 – 10x + 13 = y

roots of this quadraticare not sweet!

not factorable

How do we determine whatthe roots of this and similarquadratic equations are?

Quadratic Formula

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

b2 – 4ac - discriminantthe expression underthe radical sign

Solving Quadratics using the Formula

Quadratic Formula

x b b2 4ac

2a - two answers to quadratic

one added to -bsecond subtracted from -b

x b b2 4ac

2a

y = ax2 + bx + c quadratic instandard form

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Solving Quadratics using the Formula

Quadratic Formula

x b b2 4ac

2a

Solve: x2 – 10x + 13 = 0

x ( 10) ( 10)2 4(1)(13)

2(1)

a = 1 b = -10c = 13

x 10 48

2

x 10 48

2

x 10 16 3

2

x 10 16 3

2

x 10 4 3

2

x 10 4 3

2

x 5 2 3

y = ax2 + bx + c

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Check your answer

x2 – 10x + 13 = 0

(5 2 3)2 10(5 2 3) 13 0

25 20 3 12 50 20 3 13 0

25 + 12 – 50 + 13 = 0

0 = 0

x 5 2 3

x 5 2 3

check 2nd value of x also

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Model Problems

x2 + 2x – 24 = 0

Find the roots of each equation by usingthe quadratic formula. Express irrationalroots in simplest radical form.

2x2 + 5 = 11x

4x2 = 4x + 39

Express to nearest hundredth

{-6, 4}

{1/2, 5}

x2 + 4x = 16

{-2.66, 3.66}

{ 2 2 5 }

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

A = lw

Model Problems

The length of a rectangle is 4 more than itswidth. Find its dimensions if its area is 8.

x b b2 4ac

2a

x = width x + 4 = length

x(x + 4) = 8

x2 + 4x = 8

x2 + 4x – 8 = 0Unfactorable

a = 1, b = 4, c = -8

x (4) 42 4(1)( 8)

2(1)

x (4) 48

2

x (4) 48

2

x 2 2 3

x 2 2 3

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

A = lw

Model Problems (con’t)

The length of a rectangle is 4 more than itswidth. Find its dimensions if its area is 8.

x = width x + 4 = length

x 2 2 3

x 2 2 3negative answernot possible

width:

length ( 2 2 3) 4length = x + 4

length 2 2 3

x(x + 4) = 8 x2 + 4x – 8 = 0

Aim: Quadratic Formula Course: Adv. Alg. & Trig.

Aim: What is the quadratic formula and how do we use it?

Do Now: Solve by graphing using quadratic formula factoring2x2 = x + 15