Polynomial Functions
Suppose matrix D is the inverse of matrix C. Which of the following is equal to D?
Answer: CCC
Raj encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix c =[2 5 1 2] to get a matrix that represents the encoded text. The matrix representing the encoded text is . What is the secret phrase? Determine the location of spaces after you decode the text.
Answer: The corn is yummy.
Which statement describes how the graph of the given polynomial would change if the term -3x^6 is added? y = 2x^6 + 9x^5 - 7x^3 - 1
Answer: The ends of the graph will extend in opposite directions.
A polynomial function has a root of -6 with multiplicity 1, a root of -2 with multiplicity 3, a root of 0 with multiplicity 2, and a root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about the graph is true?
Answer: The graph of the function is positive on (-2, 4).
A polynomial function has a root of -3 with multiplicity 2, a root of 0 with multiplicity 1, a root of 1 with multiplicity 1, and a root of 3 with multiplicity 2. If the function has a positive leading coefficient and is of even degree, which could be the graph of the function?
Answer: The graph that has both ends up, has 5 touches above the x axis
What is the product? [4 3] times [-3 1] [-1 -1] [-2 2]
Answer: [-18 10] [ 5 3]
Which table describes the behavior of the graph of f(x) = 2x3 - 26x - 24?
Answer: [-infin, -3] below [-3, -1] above [-1, 4] below [4, infin] above
Jelani wrote the system of linear equations below to represent the number of student and adult tickets he and his friend sold to their school play. 12s + 10a = 128 16s + 21a = 232 Jelani also wrote the augmented matrix to represent this system. Which matrix could Jelani have written?
Answer: [12 10 128] [16 21 232]
What is the value of C in the matrix equation below? [-18 3 5] - C = [-22 1 12]
Answer: [4 2 -7]
Jonas made the following matrix of temperatures for the first 4 days of January. [6 -3 3 1] He also made the following matrix of temperatures for the first 4 days of February. [1 -3 -5 -6] Which matrix shows the difference of January and February?
Answer: [5 0 8 5]
Which is a coefficient matrix for the system of linear equations? [6a +2b=22] [-8b - 3c = -19] [-10a + 9c = -12]
Answer: [6 2 0] [0 -8 -3] [-10 0 9]
What are the values of c and d in the matrix subtraction below? [6 8] minus [c+2 3] equals [22 5] [-11 15] [-5 d-4] [-6 17]
Answer: c = -18 d = 2
Let a, b, and c be real numbers where a =/b=/ c=/ 0. Which of the following functions could represent the graph below?
Answer: f(x) = x^2(x-a)^2(x-b)^4(x-c)
What is the determinant of the coefficient matrix of the system -x - y + 2z = 5 3x + 2y - z = 3 4x + 4y - 8z = -2
Answer: zero
The graphs of two polynomial equations do not intersect. Kelly concludes that the system has no solution. Which statement best explains why Kelly's reasoning is correct or incorrect?
Answer: She is incorrect because systems may have only complex solutions which are not visible on a graph.
Which value of x makes the two matrices inverses of each other? 5 2 1 -2 2 1 x 5
Answer: -2
Carlos graphed the system of equations that can be used to solve x^3 - 2x^2 + 5x - 6 = -4x^2 + 14x + 12 What are the roots of the poly equation?
Answer: -3, -2, 3
The matrix R[12 4]represents the length of 12 in. and the width of 4 in. of a rectangle. If matrix multiplication is used to double the length and width of the rectangle, which rectangle represents the result of the matrix multiplication?
Answer: 24w x 8l
What is the determinant of A -2 2 b 0 3 a 0 0 -5
Answer: 30
A cube has side length x. One side of the cube is increased by 4 inches, and another side is doubled. The volume of the new rectangular prism is 450 cubic inches. The equation can be used to find x. What was the side length of the original cube? Use a graphing calculator and a system of equations to find the answer.
Answer: 5 inches
In the matrix below, what is the value of t32?
Answer: 8
What is the value of d21 + d22 + d23 given the matrix equation below? 1 0 1 9 -3 2 -3 9 -7 8 -1 0 -20 2 4 11 15 3
Answer: 8
Which of the following sets of data would you likely represent with a square matrix?
Answer: A racquetball club has a tournament where each member plays every other member and represents the scores in a matrix.
