Algebra II: Unit 1
The graph of the function f(x) = -(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The function is positive____________.
for no values of x
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x - 3)? (0,6) (0,-6) (6,0) (-6,0)
d
What is the vertex of the quadratic function f(x) = (x - 8)(x - 2)?
5, -9
Which function has two x-intercepts, one at (0, 0) and one at (4, 0)? f(x) = x(x − 4) f(x) = x(x + 4) f(x) = (x − 4)(x − 4) f(x) = (x + 4)(x + 4)
a
Graph the function f(x) = (x + 1)(x - 5). Use the drop-down menus to complete the steps needed to graph the function. 1: Identify the x-intercepts: (-1, 0) and (5, 0) 2: Find the midpoint between the intercepts: (2, 0) 3: Find the vertex? a(1, -8) b(2, -9) c(2, -5) d(3, -4) 4: Find the y-intercept? 5: Plot another point, then draw the graph.
b
What is the square root of -1? -i i -1 1
b
What is the sum of √-2 and √-18? 4√2 4√2i 5√2 5√2i
b
What is the y-intercept of the quadratic functionf(x) = (x - 6)(x - 2)? (0,-6) (0,12) (-8,0) (2,0)
b
Which point is an x-intercept of the quadratic function f(x) = (x - 4)(x + 2)? (-4, 0) (-2, 0) (0, 2) (4, -2)
b
In which quadrant is the number -14 - 5i located on the complex plane? I II III IV
c
Zander was given two functions: the one represented by the graph and the function f(x) = (x + 4)2. What can he conclude about the two functions? They have the same vertex. They have one x-intercept that is the same. They have the same y-intercept. They have the same range.
c
The graph of the function f(x) = -(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The function is decreasing____________.
when x>1
Simplify each of the following powers of i by the power of 162=
-1
Simplify each of the following powers of i by the power of 15. = i -i 1 -1
-i
What is the equation of the quadratic function with a vertex at (2,-25) and an x-intercept at (7,0)? f(x) = (x - 2)(x - 7) f(x) = (x + 2)(x + 7) f(x) = (x - 3)(x + 7) f(x) = (x + 3)(x - 7)
d
The graph of the function f(x) = -(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The range of the function is__________________.
all numbers </= 0
Express the following in simplest a + bi form. √9+√-36 a: -9i b: 3-6i c: 3+6i d: 9i
b
Which of the following is a complex number? -7 2+√3 4 + 9i π
c
If f(x) = x by the power of 3 - 2x by the power of 2, which expression is equivalent to f(i)? -2 + i -2 - i 2 + i 2 - i
d
Select the expression that is equivalent to |4-3i| . 1 √7 5i 5
d
The function f(x) = (x − 4)(x − 2) is shown. What is the range of the function? all real numbers less than or equal to 3 all real numbers less than or equal to −1 all real numbers greater than or equal to 3 all real numbers greater than or equal to −1
d
The graph of the function f(x) = (x - 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x wherex < 0. The function is increasing for all real values of x wherex < -1 and where x > 4. The function is decreasing for all real values of x where-1 < x < 4. The function is decreasing for all real values of x wherex < 1.5.
d
Which complex number has a distance of √17 from the origin on the complex plane? 2 + 15i 17 + i 20 - 3i 4 - i
d
Which pair of complex factors results in a real-number product? 15(-15i) 3i(1-3i) (8 + 20i)(-8 - 20i) (4+7i)(4-7i)
d
Which expression is equivalent to √80? -4√5 -4√5i 4√5 4√5i
c
Which function has a vertex at (2, -9)? f(x) = -(x - 3)2 f(x) = (x + 8)2 f(x) = (x - 5)(x + 1) f(x) = -(x - 1)(x - 5)
c
The graph of the function f(x) = -(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The domain of the function is___________.
all real numbers
What is the y-intercept of the quadratic functionf(x) = (x - 8)(x + 3)? (8,0) (0,3) (0,-24) (-5,0)
c
Which complex number is represented by the point graphed on the complex plane below? -4 + 3i 3 + 4i 3 - 4i 4 + 3i (dot in the quatrant IV)
c
Simplify each of the following powers of i by the power of 99= i -i 1 -1
-i
√−100=
0+10i
Simplify each of the following powers of i by the power of 32= i -i 1 -1
1
Graph the function f(x) = (x + 1)(x - 5). Use the drop-down menus to complete the steps needed to graph the function. 1: Identify the x-intercepts: (-1, 0) and (5, 0) 2: Find the midpoint between the intercepts: (2, 0) 3: Find the vertex? 4: Find the y-intercept? a(0, -9) b(0, -5) c(0, 4) d(0, 5) 5: Plot another point, then draw the graph.
b
The graph of the function f(x) = (x + 6)(x + 2) is shown. Which statements describe the graph? Check all that apply. The vertex is the maximum value. The axis of symmetry is x = -4. The domain is all real numbers. The function is increasing over (-∞, -4). The function is negative over (-6, -2).
b,c,f
Mr. Walker gave his class the function f(x) = (x + 3)(x + 5). Four students made a claim about the function. Each student's claim is below. Jeremiah: The y-intercept is at (15, 0). Lindsay: The x-intercepts are at (-3, 0) and (5, 0). Stephen: The vertex is at (-4, -1). Alexis: The midpoint between the x-intercepts is at (4, 0). Which student's claim about the function is correct? The claim by [ a:Jeremiah b:Lindsay c:Stephen d:Alexis] is correct.
c
Think about plotting points in the complex plane to represent the following numbers: -3+8i 4i 6 5-2i Where is each point located on the graph? -3 + 8i is___________ a)on the horizontal axis b)on the vertical axis c)in quadrant I d)in quadrant II. 4i is_____________ e)on the horizontal axis f)on the vertical axis g)in quadrant I h)in quadrant IV. 6 is_______________ i)on the horizontal axis j)on the vertical axis k)in quadrant I l)in quadrant IV. 5 - 2i is___________ m)on the horizontal axis n)on the vertical axis o)in quadrant III p)in quadrant IV.
d,f,i,p
The graph of the function f(x) = -(x + 1)2 is shown. Use the drop-down menus to describe the key aspects of the function. The vertex is the_______.
maximum value