BLOCK 2 REVIEW

Operations with Radicals and Radical Functions and Equations

100

Express the answer (5 - 6i) (11 +3i) in terms of i

73 -51i

200

Simplify using positive exponents only;

(-4w¹⁴c^-19t¹³) (-3w¹⁸c^-16)

12w³²t¹³ / c³⁵

300

Solve the equation; 

(8x + 12)^1/2 - 3 = x

X= 3; not extraneous

X= -1 not extraneous

400

Solve ; 2(x-10)^-1/3 = 3

x = 278/27

500

Solve; 

x^2/3+5x^1/3 + 4 = 0

x = -64, -1

Quadratic Equations

100

Put y = x²+18x+80 into vertex form

(x+9)²-1

200

Put equation y = -3 ( x-2)² - 1 in general form

y = -3x +12x - 13

300

Determine f(x)= 9x²- 49

A) The vertex

B) The y -intercept

C) The x - intercept

a) (0,-49)

B)(0,-49)

C) (7/3,0) , (-7/3 , 0)

400

Determine f(x) = 2(x-5)²-1

A) the vertex

B)the y - intercept

C) the x - intercept

D) Axis of Symmetry

a) (5,-1)

B)(0,49)

C)(10 + and - square root (2) /2 ,0) 

D) x = 5

500

The height y, in ft , of a ball thrown by a child is y = -1/12x² + 2x + 5 

Where x is the horizontal distance in feet from the point at which the ball is thrown. 

A) How high is the ball when it leaves the child’s hand?

B)What is the maximum height of the ball?

a)5 feet

B) 17 feet

Quadratic Equations and Inequalities

100

Solve x using square root property

10(x-7)²+19 = 379

x=13,1

200

Solve using quadratic formula

-4x² + 7x + 15 = 0

x = 3, -5/4

300

Solve inequality

5x² + 9x - 2 smaller than equal to 0 

[-2,1/5]

400

Solve inequality 

3x² + 8x + 1 smaller than equal to 0 

[ -4 (-)(+) square root (13) / 3]

500

Solve inequality

3x²+13x+3 greater than 0

(-oo , -13 - square root (133) / 6 ) U ( -13 +sqaure root (133) /oo)

Higher Order Polynomials

100

Given Polynomial p(x) = -1/5 (x+3) (x-1)²(x-3)²

Determine the following:

A) Degree

B) Degree of polynoamial

C) y - intercept

D) How many turning points

E) State the zeroes from lowest to highest and their multiplicity

a) 5

B) odd

C) (0, -27/5)

D) 4 

5) -3 = 1 ; 1 = 2 ; 3 =2

200

²Divide polynomials

(x³+5x²-7x+2) / x-2

x²+7x+7 remainder 16

300

Divide polynomial

27a⁴+87a³+30a²+66a-5 / 9a²+2a+7

3a³+9a-1 remainder 5a+2

400

Divide polynomial

X⁴-x³-6x+8 / x-2

x³+x²+2x-2 remainder 4

500

Divide using synthetic division 

-8x³-12x²+28x - 7 / 2x-1

-4x²-8x + 10 remainder 3

Higher Order Polynomials Equations Creating Polynoamials

100

Given x=5 x=-2 as zeroes of the polynomial

Y=x⁴-x³-18x²-14x+20

Find the rest of the zeroes

-1 (+)(-) square root 3

200

Find all solutions to the equation

0 = 2x⁴-3x³+30x²-48x-32

x= -1/2,2,-4i,4i

300

Find all zeroes 

Y = x⁴+x³-23x²-35x

0,5,-3+square root (2),-3 - square root (2)

400

Write a polynomial with leading coefficient 1, degree 5, zeroes at x=i , x=5-i , that passes through the origin. Write the function using only real values.

x(x²+1)(x²-10x+26)

500

Write a polynomial with degree 4 that has a zero at x=-3-i square root (2) and a zero at x = -5 with multiplicity of two using only integers. 

p(x)= x⁴+16x³+96x²+260x+275