Quadratics

Solve by Factoring

100

X^2 + 2X + 1 = 0

(X+1)(X+1) = 0 ---> X = -1

200

x^2 - 4 = 0

(X-2)(X+2) = 0 ------> X = 2, -2

300

49X^2 - 1 = 0

(7X+1)(7X-1) = 0 --------->X = 1/7, -1/7

400

13X^2 - 54x + 8

(13X - 2)(X - 4) = 0 -----------> x = 4, 2/13

500

-24X^2 + 69x - 45

(8X - 15)(-3x + 3) = 0

Quadratic Formula

100

What is the quadratic formula?

-b +/- sqrt(b^2 - 4ac) __________________ 2a

200

What is the discriminant?

b^2 - 4ac

300

X^2 + 11X +11 = 0

(-11 +/- (sqrt 77)) / 2

400

X^2 + -12X = 7

6 +/- sqrt43

500

-3X^3 + 14X^2 = X

(7 +/- (sqrt 46)) / 3, 0

Composition of Functions

100

if f(x) = -3x + 9 What is f(3)?

0

200

if f(x) = x/3 and g(x) = 2x+1 What is f(g(-2))?

-1

300

If f(x) = x/8 - 5/8 and g(x) = x/2 What is f(g(x))?

(x-10) / 16

400

If a(x) = 1/x and b(x) = x/3 and c(x) = x/3 and d(x) = 9x What is (a(b(c(d(x))))?

1/x

500

If f(x) = x^2 + 6x and g(x) = 12 - x What is f(g(x))? (answer must be factored into simplest form)

(x-18)(x-12)

Find the Inverse

100

y = x +1

y = x - 1

200

y = -3x - 7

y = (x+7)/(-3)

300

y = (x + 4) / (3x-5)

y = (5x +4) / (3x - 1)

400

y = sqrt(x + 25) / 4

y = (4x + 5)(4x - 5)

500

If f(x) = (x^2) - 4/3 and g(x) = 3x + 4 Find f^-1(g^-1(x))

sqrt(x/3)

Negative Roots

100

Simplify sqrt (-7)

i sqrt(7)

200

Simplify sqrt(-121)

i(11)

300

Simplify sqrt(-243)

(9)(i)sqrt(3)

400

Solve via Quadratic Formula: x^2 + 3X + 3

(-3 +/- (i)(sqrt3)) / 2

500

2X^2 - 4x = -7

1 +/- i (sqrt10)/2