Radicals
More Radicals
Solve Quadratic Equations
a+bi
Graph Quadratic Functions (do in order*)
100
Simplify. Write the solution in radical notation.
sqrt(48a^9b^2c)
4a^4bsqrt(3ac)
100
Find the domain of the square root function and express in interval notation:
g(x)=sqrt(-5x-2)
(-infty,-2/5]
100
Solve for x and check:
sqrt(6x+7)-x=2
{-1,3}
100
Simplify and express in a+bi form:
(2+6i)-(12-4i)
-10+10i
100
1. For the function
f(x)=x^2-4x-5
Determine the coordinates of the x-intercepts
(5,0) and (-1,0)
200
Simplify:
5sqrt(45)-2sqrt(80)+sqrt28
7sqrt5+2sqrt7
200
Simplify using the properties of rational exponents. Write your answer in radical notation.
(-125a^9b^4)^(1/3)
-5a^3broot(3)(b)
200
Solve the quadratic equation only by completing the square:
x^2+4x-14=0
x=-2+-3sqrt2
200
Simplify and express in a+bi form:
(2+3i)^2
-5+12i
200
2. For the function
f(x)=x^2-4x-5
Determine the coordinates of the y-intercept.
(0,-5)
300
Simplify:
-2sqrt50+3sqrt20-9sqrt8
-28sqrt2+6sqrt5
300
Rationalize the denominator and simplify if possible:
6/(4-sqrt2)
(12+3sqrt2)/7
300
Solve the quadratic equation only by completing the square:
x^2-10x-3=0
x=5+-2sqrt7
300
Rationalize the denominator and express in a+bi form:
(2+3i)/(3-i)
3/10+11/10i
300
3. For the function
f(x)=x^2-4x-5
Find the equation of the axis of symmetry.
x=2
400
Multiply and simplify:
(sqrt5+sqrt7)(3sqrt5-2sqrt7)
1+sqrt35
400
Rationalize the denominator and simplify if possible:
2/(3-sqrt5)
(3+sqrt5)/2
400
A rectangular garden whose length is 2 feet longer than its width had an area of 66 square feet. Find the dimensions of the garden rounded to the nearest tenth. Draw and label an appropriate diagram.
width = 7.2 feet
length = 9.2 feet
400
Rationalize the denominator and express in a+bi form:
(5-2i)/(3+2i)
11/13-16/13i
400
4. For the function
f(x)=x^2-4x-5
Determine the coordinates of the vertex.
(2,-9)
500
Multiply and Simplify:
(6sqrt10-3sqrt2)(sqrt10+sqrt2)
54+6sqrt5
500
Solve for x and check:
x=sqrt(3x+7)-3
{-2,-1}
500
A rectangular window has a length that is 4 feet longer than its width. The area of the window is 90 square feet.What are the dimensions of the window, rounded to the nearest tenth? Draw and label an appropriate diagram.
width = 7.7 ft
length = 11.7 ft
500
Challenge: Solve for x.
root(3)(7x-1)=3
x=4
500
5. For the function
f(x)=x^2-4x-5
Graph the function.
