Patterns and Sequences
Key Features
Problem-Solving
Comparing Functions
100
The points (0, 5), (1, 6), (2, 9), and (3, 14) are on the graph of a function. Write an equation to represent that function.
f(x) = x2 + 5
100
Write the equation of a parabola with a vertex of (0, 0).
y = x2
100
The function g(t) = -16t2 + 75t represents the flight of a rocket, where t represents time in seconds, and g(t) represents the rocket's height.
From what height was the rocket launched?
0 feet (directly from the ground)
100
What is the minimum of the function?
-4
200
In the given sequence, determine the 15th term:
-7, -4, 1, 8, 17, ...
217
200
Write the equation of a parabola that crosses through the x-axis at (0, 0) and (4, 0).
y = x2 - 4x
200
A rectangular garden has a length that is 8 feet longer than its width. Let w represent the width of the garden, in feet. The entire garden is surrounded by a 2-foot-wide walkway.
What does the expression (w + 4)(w + 12) represent in this context?
the total area of both the garden AND walkway
200
What is the y-intercept of this function?
-16
300
What explicit expression can be used to find the nth term of this sequence:
2, 5, 10, 17, 26, ...
n2 + 1
300
Write the equation of a parabola with a vertex of (-3, 8).
y = (x + 3)2 + 8
300
A ball was thrown upward into the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the expression
-16t2 + 35t + 5
What is the meaning of the 5 in the expression?
The ball was thrown from a height of 5 feet.
300
f(x) = (x + 3)2 + 7
g(x) = x2 + 4x + 9
Which function has the greater y-intercept? What is it?
f(x) with a y-intercept of 16
f(x), with a y-intercept of 16
400
Write a function that represents f(n), the number of small squares in figure n.
f(n) = (n + 4)2
or
f(n) = n2 + 8n + 16
400
Write the equation of a parabola with x-intercepts of -7 and 5 in intercept form.
y = (x + 7)(x - 5)
400
A rectangular rug has an area of 28 square feet. The rug is 3 feet longer than it is wide.
Write an equation that can be used to determine the length and width of the rug, in standard form.
w2 + 3w - 28 = 0
400
f(x) = (x + 3)2 + 7
g(x) = x2 + 4x + 9
Which function has the greater vertex x-value? What is it?
g(x), with a vertex x-value of -2
500
Write an equation that describes the relationship of the listed ordered pairs:
(2, 1), (3, 11), (4, 25), (5, 43)
y = 2x2 - 7
500
Write the equation of a parabola with x-intercepts of -10 and 6 in standard form.
y = x2 + 4x - 60
500
A rectangle has an area of 40m2 , with a length that is 3 feet longer than its width. Using an equation, determine the length and width of the rectangle.
length of 8m
width of 5m
500
f(x) = (x + 3)2 + 7
g(x) = x2 + 4x + 9
Which function has the smaller minimum? What is it?
g(x), with a minimum of 5