Solving quadratic equations
Perfect squares
Equivalent expressions
Rational and irrational numbers
Old stuff
100
Solve the following quadratic equation:
x^2=100
x = 10 and x = -10
100
True or false: the following is a perfect square
(1/2x+4)^2
TRUE
100
Change the following to standard form
x(x+1)
x^2+x
100
True or false: This number is irrational
1/9
FALSE
100
Write the following in words
2x+5>10
Double of a number plus 5 is greater than 10
200
Solve the following quadratic equation:
x^2+19=55
x = 6 and x = -6
200
True or false: this is a perfect square
x^2-10x-25
FALSE
200
Change the following to vertex form:
x^2+6x=16
(x+3)^2=25
200
True or false: adding a rational with a rational is rational
TRUE
200
Evaluate the following when x=4:
(-3)^x
81
300
Solve the following equation:
p^2+16p+55=0
p = -11 and p = -5
300
Change the following to standard form:
(x-9)^2
x^2-18x+81
300
If you change a function to factored form, which of the following can you find? Select all that apply.
B, C and D
300
Provide an example of an irrational number times an irrational number equals an irrational number
Example:
sqrt5timessqrt7=sqrt35
300
Evaluate the following expression when z=11 and y=-2:
z+z+y^2
26
400
Solve the following equation:
2k^2+4k=96
k = 6 and k = -8
400
Solve the following equation:
(x-3)^2=1
x = 2 and x = 4
400
If you change a function to vertex form, how do you find the coordinates for the vertex?
x-coordinate: opposite of inside the parentheses
y-coordinate: outside the parentheses
400
Explain why the following number is irrational
sqrt7
Two reasons:
- the inside of the square root is NOT a perfect square
- if we assume it is rational, it does not work to write it as a fraction
400
What is the x-intercept?
(20,0)
500
Solve the following equation:
2p^2=10+8p
p = 5 and p = -1
500
Solve the following equation by completing the square
2x^2-24x=-40
x = 2 and x = 10
500
What is an equivalent form of this function that shows the zeros (intercepts) of the function?
-3x^2-21x-30
-3(x+5)(x-2)
500
Explain why the following sum is not rational
-5+sqrt6
If we say it IS rational, then we can add another rational number and it SHOULD BE RATIONAL. However, we add 5, and we get an IRRATIONAL answer.
500
Find the average rate of change between 2011 and 2014:
0.4