Radicals and Irrational Numbers
Simplify: √12
2√3
Factor completely: x2 + 7x + 12
(x + 3)(x + 4)
A quadratic function is given by
f(x) = x2 + 4x - 5
Without graphing, find the vertex of the quadratic.
(-2,-9)
Solve for x:
x2 - 7x + 12 = 0
x = 3, 4
A ball is thrown into the air. Its height is modeled by
h = -t2 + 6t + 7
where h is the height in feet and t is the time is seconds. After how many seconds will the ball hit the ground?
7 seconds
Simplify: √20 + √5
3√5
Factor completely: x2 - 9x + 20
(x - 4)(x - 5)
Given
f(x) = x2 + 6x + 5
Find the vertex
(-3,-4)
Solve for x:
3x2 + 2x - 8 = 0
x = 4/3, -2
A basketball is thrown upward. Its height is modeled by
h = -t2 + 8t + 9
where h is the height in feet and t is the time in seconds. After how many seconds will the basketball hit the ground?
9 seconds
Simplify: √45 + √20
5√5
Factor completely: 2x2 + 9x + 4
(2x + 1)(x + 4)
When given
f(x) = 2x2 - 12x + 10
Find the vertex and whether the vertex is maximum or minimum
(3,-8)
Minimum
Solve for x:
2x2 - 7x - 15 = 0
x = -3/2, 5
A rectangular garden has an area of 96 square feet. Its length is 4 feet longer than its width. What are the dimensions of the garden?
The length is 12 feet and the width is 8 feet.
Simplify: √50 - √8
3√2
Factor completely: 8x2 + 22x + 15
(2x + 3)(4x + 5)
When given
f(x) = 2x2 + 4x - 6
Find the vertex and whether is maximum or minimum.
(-1,-8)
Minimum
Solve for x:
6x2 + x - 12 = 0
x = -3/2, 4/3
A ball is thrown upward from a height of 5 feet. Its height is modeled by
h = -t2 + 10t + 5
where h is the height in feet and t is the time in seconds. After how many seconds will the ball hit the ground?
10.5 seconds
Simplify: √48 + √27 - √12
5√3
Factor completely: 12x2 + 31x + 20
(3x + 4)(4x + 5)
When given
f(x) = 3x2 - 12x - 15
Find the vertex and whether it's a minimum or maximum.
(2,-27)
Minimum
Solve for x:
8x2 - 2x - 15 = 0
x = 3/2, -5/4
A basketball is thrown from a height of 6 feet. Its height after t seconds is modeled by
h = -2t2 + 12t + 6
where h is the height in feet. After how many seconds will the basketball hit the ground?
6.5 seconds