Factoring
What are the solutions to the following equations: (x - 2)2 + 45 = 0?
No real solutions
Solve for x for: x + 2 = 5.
x = 3
What does the 5 stand for in 2nd, Trace, 5 (Hint: where does a solution to a system happen?)
Intersection(s)
What is x when |-3| = x?
x = 3
What axis do x-intercepts cross?
Which of the following is a linear factor of 2x4+x3-29x2-34x+24?
A. (x - 4)
B. (x - 3)
C. (2x + 1)
D. (x - 2)
A. (x - 4) is the linear factor.
Solve for x: 7x - 3 = 25.
x = 4
Solve the system:
y = (x + 2)2 - 5
y = -1
x = -4 and x = 0
Solve the following absolute value equation: |x| = 6.
x = -6 and x = 6
What letters does the vertex provide in the equation y = a(x - h)2 + k?
(h, k)
Factor the following completely: x4 - 8x2 + 15.
(x2 - 3)(x2 - 5)
Solve for the inverse of the linear function: f(x) = 0.25x - 2.
f-1(x) = 4x + 8
Write down the calculator steps to solve a matrix.
Press 2nd, x-1, move right, go down to B:rref(, and hit enter
Press alpha, zoom, and enter the correct size of the matrix
Type in the values of the matrix and press enter
Solve the following absolute value equation: |x - 5| = 12.
x = -7 and x = 17
Describe the transformations of the graph f(x) when f(x) is replaced by 2f(x - 3) + 5.
Vertical stretch by 2
Right 3
Up 5
Factor the following quadratic completely: 256x4 - 81.
(4x - 3)(4x + 3)(16x2 + 9)
A polynomial of degree three divided by a polynomial of degree one is shown:
(6x3 - 7x2 + 11x - 21) / (2x - 3).
Which expression best represents the simplified quotient of the division?
A. 3x2 - x + 7
B. 3x2 + 2x + 10
C. 3x2 - 2x + 10
D. 3x2 + x + 7
D. 3x2 + x + 7
Solve the following system of 3 equations using any method:
3x + y - z = -1
x + 2y + z = 0
x - 7z = -26
(2, -3, 4)
Solve the following absolute value equation: |x - 2| + 4 = 3.
No real solutions.
What are the domain and range of the following function in interval notation?
f(x) = -1/3 * (x + 5)2 - 4
Domain: (-∞ , ∞)
Range: (-∞ , -4]
A student asked Mrs. Hawkins how old she was. Mrs. Hawkins answered by saying "If you square my age and then subtract thirty-two times my age it equals 68."
How old is Mrs. Hawkins?
Mrs. Hawkins is 34 years old.
Which equation matches with a parabola with x-intercepts at 5 and -3 and passes through the point (0, -3)?
A. f(x) = 2(x - 5)(x + 3)
B. f(x) = 2(x + 5)(x - 3)
C. f(x) = 0.2(x - 5)(x + 3)
D. f(x) = 0.2(x + 5)(x - 3)
C. f(x) = 0.2(x - 5)(x + 3)
A stadium has 12,000 seats, divided into box seats, lower-deck seats and upper-deck seats. Box seats sell for $12, lower-deck sell for $10, and upper-deck seats sell for $6. When all the seats are sold, the total revenue is $97,500. The stadium has five times as many upper-deck seats as box seats. Solve for the number of lower-deck seats in the stadium.
4,500 lower-deck seats
Solve the absolute value linear equation: (5/2)|2x + 2| - 4 = 16.
x = -5 and x = 3
Which parent functions from the list below have a domain and range of all real numbers? Write all that apply.
A. y = x
B. y = x2
C. y = √ (x)
D. y = x3
E. y = 3√ (x)
F. y = |x|
A, D, and E