Unit: Quadratics and Complex Numbers

What is one solution of the following system?

(-6, 0)

How does the graph of y = a(x - h)2 + k change if the value of h is doubled?

The vertex of the graph moves to a point twice as far from the y-axis.

Which equation shows an example of the associative property of addition?

(-4 + i) + 4i = -4 + (i + 4i)

What is the value of the product (3 - 2i)(3 + 2i)?

13

Which of the following is equivalent to 18 - √ -25

18 - 5i

How many solutions exist for the system of equations in the graph?

2

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

Which equation is part of solving the system by substitution?

4(11 - y)^2 - 3y^2 = 8

Which expression is equivalent to √-80 ?

4√ 5i

What is the sum of √-2 and √-18?

4√2i

Which graph shows a system of equations with exactly one solution?

D

Donte simplified the expression below. What mistake did Donte make?

He did not apply the distributive property correctly for 4(1 + 3i).

In which quadrant is the number -14 - 5i located on the complex plane?

III

Parabola A can be represented using the equation (x + 3)^2 = y, while line B can be represented using the equation y = mx + 9. Isabel claims one solution to the system of two equations must always be the vertex of parabola A.Which best describes the reasonableness of her claim?

Isabel is incorrect because the point of intersection between line B and parabola A that can be determined is the y-intercept of the equations, not the vertex.

Consider the following system of equations. Which statement describes why the system has infinite solutions?

The equations represent circles that result in the same graph.

The center of a circle is at the origin on a coordinate grid. The vertex of a parabola that opens upward is at (0, 9). If the circle intersects the parabola at the parabola's vertex, which statement must be true?

The maximum number of solutions is one.

The vertex of a parabola is in the first quadrant of a coordinate grid. A line with a negative slope passes through the origin. If the parabola and line intersect at the origin, which statement must be true?

The parabola opens downward.

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?

b^2 / 4a^2

Which property of multiplication is shown below? If x = a + bi and y = c + di, x × y = y × x.

commutative property

Which expression is equivalent to i^233?

i

During a pumpkin launching contest, two pumpkins are launched at the same time. The path of pumpkin A is modeled by the equation y = -0.01x2 + 0.32x + 4. The path of pumpkin B is modeled by the equation y = -0.01x2 + 0.18x + 5. If x represents the distance the pumpkin traveled in feet and y represents height of the pumpkin in feet, what does the intersection point of the equations represent?

the horizontal distance of the pumpkins from the launch site when their heights are the same

During a baseball game, a player hits a ball while a bird is flying across the field. Let t be the time in seconds since the ball is hit and h be the height in feet. The height of the baseball over time is modeled by the equation h = -16t2 + 65t and the height of a bird over time is modeled by the equation h = 8t + 20. What do the intersection points of the equations represent?

the time when the height of the ball and the bird are the same

Christian is rewriting an expression of the form y = ax2 + bx + c in the form y = a(x - h)2 + k. Which of the following must be true?

the value of a remains the same

Solve for x in the equation x^2 + 10x + 12 = 36

x = -12 or x = 2

What are the solution(s) of x^2 - 4 = 0

x = -2 or x = 2

Which equation has a graph that is a parabola with a vertex at (5, 3)?

y = (x - 5)^2 + 3

Which equation is the inverse of y = 16x2 + 1?

y = +- √ x - 1 ------------- 4

Which equation is the inverse of 2(x - 2)2 = 8(7 + y)?

y = +- √28 + 4x

Which equation could generate the curve in the graph below?

y = -2x^2 - 16x- 28

Which equation is y = -3x2 - 12x - 2 rewritten in vertex form?

y = -3(x + 2)2 + 10

When graphed, which parabola opens downward?

y = -3x2

Which equation is y = -6x2 + 3x + 2 rewritten in vertex form?

y = -6 ( x - 1/4 )^2 + 19/8

Which equation is y = 3(x - 2)^2 - (x - 5)^2 rewritten in vertex form?

y = 2 ( x - 1/2 )^2 - 53/4

Which equation represents a graph with a vertex at (1, -6)?

y = 3x^2 - 6x - 3

Which equation is y = 6x^2 + 12x - 10 rewritten in vertex form?

y = 6(x + 1)^2 - 16

What are the solutions of the following system?

(0, -5) and (-4, 3)

What are the solutions of the following system?

(6, 312) and (-6, 312)

Which equation demonstrates the additive identity property?

(7 + 4i) + 0 = 7 + 4i

Which equation illustrates the identity property of multiplication?

(a + bi) × 1 = (a + bi)

What are the solutions to the following system?

(√2,-1) and (-2√-1)

Which expression is equivalent to (4 + 6i^)2?

-20 + 48i

What is the first step when rewriting y = -4x^2 + 2x - 7 in the form y = a(x - h)^2 + k?

-4 must be factored from -4x^2 + 2x

What is the additive inverse of the complex number 9 - 4i?

-9 + 4i

If i = √ -1 , what is the value of i^3?

-i

What is the domain of the function ?

0 ≤ x < infinity

For which value of m does the graph of y = 18x^2 + mx + 2 have exactly one x-intercept?

12

Using the quadratic formula to solve 11x2 - 4x = 1, what are the values of x?

2/11 +- √15/11

Dimitri is solving the equation x2 - 10x = 21. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?

25

What is the discriminant of 9x^2 + 2 = 10x?

28

Which complex number is represented by the point graphed on the complex plane below?

3 - 4i

Which complex number has a distance of √ 17 from the origin on the complex plane?

4 - i

Using the quadratic formula to solve 5x = 6x^2 - 3, what are the values of x?

5 ± √ 97 / 12

What is the first step when rewriting y = 6x^2 + 18x + 14 in the form y = a(x - h)^2 + k?

6 must be factored from 6x^2 + 18x

Find the discriminant of 3x^2 - 10x = -2

76

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?

8 + i

If x = 6 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the equation?

The discriminant is 0.

Which property of addition is shown below? a + bi + c + di = a + c + bi + di

commutative property

Which could be the function graphed below?

f(x)= √x + 4

What is the square root of -1?

i

Which property of addition is shown below? If x = a + bi and y = -a - bi, x + y = 0.

inverse property

For what values of m does the graph of y = mx2 - 5x - 2 have no x-intercepts?

m < -25/8

solve for x in the equation x^2 + 4x - 4 = 8

x = -6 or x = 2

solve for x in the equation x^2 + 14x + 19 = -96

x = -7 ± 8i

solve for x in the equation x^2 - 4x - 9 = 29

x = 2 ± √42

Solve for x in the equation 3x^2 - 18x +5 = 47

x = 3 +- √5

What are the solutions of x^2 + 6x - 6 = 10

x = 8 or x = -2

What is the domain of the square root function graphed below?

x≥0

Which equation has a graph that is a parabola with a vertex at (-1, -1)?

y = (x + 1)^2 - 1

Which system is equivalent to { (y=9x^2) / ( x+y=5 )

{ (5-x=9x^2) / ( y=5-x )

What is the distance from the origin to point A graphed on the complex plane below?

√13