quadratics and complex numbers
Which equation can be solved using the expression for x? 10x^2 = 3x + 2 2 = 3x + 10x^2 3x = 10x^2 - 2 10x^2 + 2 = -3x
2 = 3x + 10x^2
Solve for x in the equation x^2-12x+59=0
x= 6 plus minus squareroot 23i
Which phrase best describes the translation from the graph y = (x + 2)2 to the graph of y = x2 + 3? 2 units left and 3 units up 2 units left and 3 units down 2 units right and 3 units up 2 units right and 3 units down
2 units right and 3 units up
What is the value of the product (3 - 2i)(3 + 2i)? 5 9 + 4i 9 - 4i 13
13
Express the following in simplest a + bi form. squareroot 9 + squareroot -39 -9i 3-6i 3+6i 9i
3+6i
What is the square root of -16? -8i -4i 4i 8i
4i
In which quadrant is the number -14 - 5i located on the complex plane? I II III IV
III
Solve for in the equation . x^2+10x+12=36 x = -12 or x = 2 x = -11 or x = 1 x = -2 or x = 12 x = -1 or x = 11
x = -12 or x = 2
Which equation is the inverse of 2(x - 2)2 = 8(7 + y)?
y=2 +_ squareroot 28+4x
Select the correct answer from the choices given(13 + 4i) + n = 0What is n? 0 1 -13 + 4i -13 - 4i
-13 - 4i
Simplify each of the following powers of i. = i✔ -i1-1 = i-i✔ 1-1 = i✔ -i1-1 = i-i1✔ -1
.
√−100 = + i
0 + 10 i
What is the first step when rewriting y = 6x2 + 18x + 14 in the form y = a(x - h)2 + k? 16 must be factored from 18x + 14 x must be factored from 6x2 + 18x 6 must be factored from 6x2 + 14 6 must be factored from 6x2 + 18x
6 must be factored from 6x2 + 18x
Solve x2 - 16x + 60 = -12 by completing the steps. First, subtract _____from each side of the equation. Next, add ____to each side of the equation to complete the square.
60 64
If , i= squareroot -1 what is the value of i^3? -1 i 1 -i
-i
(9 - 6i) × m = 9 - 6iWhat is m? 0 1 9 + 6i -9 + 6i
1
If f(x) = 1 - x, which value is equivalent to |f(i)|? 0 1 squareroot 2 squareroot -1
squareroot 2
Evaluate (2-5i)(p+q)(i) when p=2 and q=5i 29i 29i-20 -21i 29
29i
3x = 0.5x2 x = -6 or x = 0 x = -4 or x = 3 x = -2 or x = 1.5 x = 0 or x = 6
x = 0 or x = 6
Given (x - 7)2 = 36, select the values of x. x = 13 x = 1 x = -29 x = 42
x = 13 x = 1
Which could be the function graphed below?
f(x) = squareroot x-2
0 = 5x2 - 2x + 6
x= 1 plus minus i squareroot 29 / 5
Which expression is equivalent to squareroot -80 ? -4 squareroot 5 -4 squareroot 5i 4 squareroot 5i 4 squareroot 5
4 squareroot 5i
Choose the equation that represents the solutions of 0 = 0.25x2 - 8x.
x= (8 squareminus squareroot (-8)^2 - (4)(0.25)(0)/ 2(0.25)
Solve for in the equation x^2+2x+1=17
x= -1 plus minus squreroot 17
Multiply and simplify the product.(8 - 5i)2Select the product. 39 89 39-80i 89-80i
39-80i
In the derivation of the quadratic formula by completing the square, the equation(x+(b/2a))^2 = (-4ac+b^2)/ (4a^2) is created by forming a perfect square trinomial.What is the result of applying the square root property of equality to this equation?
x+ (b/2a) = (plus minus squareroot b^2 -4ac) / 2a
Subtract (3 + 2i) from (-9 - 8i). -17 - 5i -6 - 6i -12 - 10i 12 + 10i
-12 - 10i
Which value must be added to the expression x2 + 16x to make it a perfect-square trinomial? 8 32 64 256
64
Which equation is the inverse of y = 2x2 - 8?
A. y= squaretoot x=8/2
When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial? x^2+ (b/a)x +_ = (-c/a)+_
b^2/ 4a^2
What values of c and d would makethe following expression represent a real number?i(2 + 3i)(c + di) c = 2, d = 3 c = -2, d = 3 c = 3, d = -2 c = -3, d = -2
c = -3, d = -2
Using the quadratic formula to solve x2 = 5 - x, what are the values of x?
(-1 plus minus squareroot 21 )/2
Which pair of complex factors results in a real-number product? 15(-15i) 3i(1-3i) (8 + 20i)(-8 - 20i) (4+7i)(4-7i)
(4+7i)(4-7i)
Which addition expressionhas the sum 8 - 3i ? (9 + 2i) + (1 - i) (9 + 4i) + (-1 - 7i) (7 + 2i) + (1 - i) (7 + 4i) + (-1 - 7i)
(9 + 4i) + (-1 - 7i)
Which equation illustrates the identity property of multiplication? (a + bi) × c = (ac + bci) (a + bi) × 0 = 0 (a + bi) × (c + di) = (c + di) × (a + bi) (a + bi) × 1 = (a + bi)
(a + bi) × 1 = (a + bi)
Complete the expression so it forms a perfect-square trinomial. x² - 5x + 5/25/4✔ 25/4 x² + ✔ 1477/2 x + 49
.
Simplify each expression. Select the correct answer from the drop-down menu. −6(3i)(−2i) = ✔ -36 2(3 − i)(−2 + 4i) = ✔ -4 + 28i
.
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 on the horizontal axison the vertical axisin quadrant I✔ in quadrant II. 4i is on the horizontal axis✔ on the vertical axisin quadrant Iin quadrant IV. 6 is ✔ on the horizontal axison the vertical axisin quadrant Iin quadrant IV. 5 - 2i is on the horizontal axison the vertical axisin quadrant III✔ in quadrant IV.
.
Which phrase best describes the translation from the graph y = 6x2 to the graph of y = 6(x + 1)2? 6 unit left 6 unit right 1 unit left 1 unit right
1 unit left
Let x = a + bi and y = c + di and z = f + giWhich statements are true? Check all of the boxes that apply. x + y = y + x (x × y) × z = x × (y × z) x - y = y - x (x + y) + z = x + (y + z) (x - y) - z = x - (y - z)
1. x + y = y + x 2. (x × y) × z = x × (y × z) 4. (x + y) + z = x + (y + z)
Multiply and simplify the product.(3 - 5i)(-2 + 4i)Select the product. 14+ 2i 14 + 22i 15 + 22i 26+2i
14 + 22i
What is the first step when rewriting y = 3x2 + 9x - 18 in the form y = a(x - h)2 + k? 3 must be factored from 3x2 + 9x x must be factored from 3x2 + 9x 9 must be factored from 9x - 18 3 must be factored from 3x2 - 18
3 must be factored from 3x2 + 9x
Multiply and simplify the product.-12i × 3iSelect the product. 36 -36 36i -36i
36
Which of the following is an example of a complex number that is not in the set of real numbers? -7 2 + squareroot 3 4 + 9i pie
4 + 9i
Which complex number has a distance of squareroot of 17 from the origin on the complex plane? 2 + 15i 17 + i 20 - 3i 4 - i
4 - i
What is the sum of squareroot of -2 and squareroot of-18 4 squareroot 2 4 squareroot 2i 5 squareroot 2 5 squareroot 2i
4 squareroot 2i
Which phrase best describes the translation from the graph y = 2(x - 15)2 + 3 to the graph of y = 2(x - 11)2 + 3? 4 units to the left 4 units to the right 8 units to the left 8 units to the right
4 units to the left
Multiply each pair of factors. Type the product in the space provided. (6 + 3i)(6 − 3i) = (4 − 5i)(4 + 5i) = (−3 + 8i)(−3 − 8i) =
45 41 73
Which of the following expressions are perfect-square trinomials? Check all of the boxes that apply. x2 - 16x - 64 4x2 +12x + 9 x2 + 20x + 100 x2 + 4x + 16
4x2 +12x + 9 x2 + 20x + 100
Select the expression that is equivalent to . | 4-3 | 1 squareroot 7 5i 5
5
Find the sum of (-4 + i) and (10 - 5i). -3 + 5i -3 - 5i 6 - 4i 6 - 6i
6 - 4i
Now, write x² - 16x + 64 = -8 as ✔ (x - 8)² = -8
8 2
The relationship between voltage, E, current, I, and resistance, Z, is given by the equation E = IZ. If a circuit has a current I = 3 + 2i and a resistance Z = 2 - i, what is the voltage of the circuit? 4 - i 4 + i 8 + i 8 + 7i
8 + i
Aiko is finding the sum (4 + 5i) + (-3 + 7i). She rewrites the sum as (-3 + 7)i + (4 + 5)i. Which statement explains the error Aiko made by using a mathematical property incorrectly? Aiko incorrectly used the commutative property by changing the order of the two complex numbers. Aiko incorrectly used the associative property by changing the order of the two complex numbers. Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part. Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part.
Which of the statements about the following quadratic equation is true?6x2 - 8 = 4x2 + 7x The discriminant is greater than zero, so there are two real roots. The discriminant is greater than zero, so there are two complex roots. The discriminant is less than zero, so there are two real roots. The discriminant is less than zero, so there are two complex roots.
The discriminant is greater than zero, so there are two real roots.
If the discriminant of a quadratic equation is equal to , which statement describes the roots? There are two complex roots. There are two real roots. There is one real root. There is one complex root.
There are two complex roots.
Which property of multiplication is shown below?If x = a + bi and y = c + di, x × y = y × x. commutative property identity property distributive property associative property
commutative property
Which expression is equivalent to i^233? 1 -1 i -i
i
Which property of addition is shown in the equation below?a + bi + 0 + 0i = a + bi commutative property inverse property identity property associative property
identity property
Which property of addition is shown below?If x = a + bi and y = -a - bi, x + y = 0. commutative property identity property associative property inverse property
inverse property
What is the distance from the origin to point A graphed on the complex plane below? squareroot 5 squareroot 13 9 13
squareroot 13
Solve for in the equation .x^2+14x+17=-96 x= -7 plus minus 4 squareroot 6i x = -7 ± 8i x= 7 plus minus 4 squareroot 6i x = 7 ± 8i
x = -7 ± 8i
Which equation can be simplified to find the inverse of y = 2x2?
x = 2y2
Which equation can be simplified to find the inverse of y = 5x2 + 10?
x = 5y2 + 10
What is the domain of the function y= sqaureroot x+ 6-7
x greater or equal to -6
What is the domain of the square root function graphed below?
x is greater to or equal to 3
If , f(x)= squareroot x-3 which inequality can be used to find the domain of f(x)?
x-3 greater or equal to 0
Which equation shows the quadratic formula used correctly to solve 5x^2 + 3x - 4 = 0 for x?
x= (-3 plus minus squareroot (3)^2-4(5)(-4)/ 2(5)
Use completing the square to solve for in the equation .(x+7)(x-9)=25 x = -4 or 6 x = -2 or 14 x= 1 plus minus squareroot 89 x= 1 plus minus squareroot 87
x= 1 plus minus squareroot 89
Given (x - 1)2 = 50, select the values of x. x = -49 x = 51 x= 1+5 squareroot 2 x= 1-5 squareroot 2
x= 1+5 squareroot 2 x= 1-5 squareroot 2
What are the solutions of x^2+6x-6=10 x=-11 or x=1 x=-11 or x=-1 x=-8 or x=-2 x=-8 or x=2
x=-8 or x=2
Solve for in the equation x^2-10x+25=35
x=5 plus minus squareroot 35
Which equation has a graph that is a parabola with a vertex at (-1, -1)? y = (x - 1)2 + 1 y = (x - 1)2 - 1 y = (x + 1)2 + 1 y = (x + 1)2 - 1
y = (x + 1)2 - 1
Which equation has a graph that is a parabola with a vertex at (5, 3)? y = (x - 5)2 + 3 y = (x + 5)2 + 3 y = (x - 3)2 + 5 y = (x + 3)2 + 5
y = (x - 5)2 + 3
Which equation is y = -3x2 - 12x - 2 rewritten in vertex form? y = -3(x + 2)2 + 10 y = -3(x - 2)2 + 10 y = -3(x + 2)2 - 14 y = -3(x - 2)2 - 2
y = -3(x + 2)2 + 10
Which equation is y = 6x2 + 12x - 10 rewritten in vertex form? y = 6(x + 1)2 - 11 y = 6(x + 1)2 - 10 y = 6(x + 1)2 - 4 y = 6(x + 1)2 - 16
y = 6(x + 1)2 - 16
Which equation is the inverse of y = 16x2 + 1?
y= squareoot x-1/4
Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form? y=2 (x+ (7/2))- 1/4 y=2 (x+ (7/2))+ 1/4 y = 2(x + 7)2 - 73 y = (x + 7)2 - 24
y=2 (x+ (7/2))+ 1/4
Which equation shows an example of the associative property of addition? (-4 + i) + 4i = -4 + (i + 4i) (-4 + i) + 4i = 4i + (-4i + i) 4i × (-4i + i) = (4i - 4i) + (4i × i) (-4i + i) + 0 = (-4i + i)
(-4 + i) + 4i = -4 + (i + 4i)
The solution to x2 - 10x = 24 is ✔ 12 or -2. The solution to 2x2 - 11 = 87 is ✔ 7 or -7 The solution to 3x2 - 12x + 24 = 0 is ✔ 2 + 2i or 2 - 2i
.
Which subtraction expressionhas the difference 1 + 4i? (-2 + 6i) - (1 - 2i) (-2 + 6i) - (-1 - 2i) (3 + 5i) - (2 - i) (3 + 5i) - (2 + i)
(3 + 5i) - (2 + i)
y = 12x2 - 9x + 4✔ no real solution(s) 10x + y = -x2 + 2✔ two real solution(s) 4y - 7 = 5x2 - x + 2 + 3y✔ no real solution(s) y = (-x + 4)2X ✔ one real solution(s)
.
Multiply and simplify the product.2i(4 - 5i)Select the product. -2i 2i -10 + 8i 10 + 8i
10 + 8i
What is the additive inverse of the complex number -8 + 3i? -8 - 3i -8 + 3i 8 - 3i 8 + 3i
8 - 3i
Brian is solving the equation x^2- (3/4)x = 5 What value must be added to both sides of the equation to make the left side a perfect-square trinomial?
9/64
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equationh = -16t2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor. t 0.87 s t 4 s t = 8.5 s t = 16 s
t=4 s
Solve for in the equation . x^2+20x+100=36 x = -16 or x = -4 x = -10 x = -8 x = 4 or x = 16
x = -16 or x = -4
