Review for Unit Test: Quadratic Functions & Complex Numbers

Multiple Select

• 10

• -10

• 10i

• -10i

Multiple Select

Simplify:

$$\sqrt[]{-25}$$  

• -5i

• 5

• 5i

• -5

Multiple Choice

Simplify:

$$\sqrt[]{-108}$$  

• $$\pm3i\sqrt{6}$$  

• $$\pm3i\sqrt{20}$$  

• $$\pm6i\sqrt{3}$$  

• $$\pm20i\sqrt{3}$$  

Multiple Choice

Simplify:

$$\sqrt[]{-49}-3\sqrt{-196}$$  

• $$-35i$$  

• $$35i$$  

• $$49i$$  

• $$-49i$$  

Multiple Choice

Simplify:

$$5\sqrt[]{-121}-2\sqrt{-36}$$  

• $$43i$$  

• $$-43i$$  

• $$67i$$  

• $$-67i$$  

Multiple Choice

Which of the following is equivalent to:

$$\sqrt[]{-12}$$  

• $$2i\ \sqrt[]{3}$$  

• $$2i\ \sqrt[]{2}$$  

• $$3i\ \sqrt[]{3}$$  

• $$3i\ \sqrt[]{2}$$  

Multiple Choice

How do you write a complex number?

• a - bi

• a + bi

• ai + b

• ai - b

Multiple Choice

What is i² equivalent to?

• -1

• √-1

• 1

• -√1

Multiple Choice

(3 + 2i) + (4 - 5i)

• 7 + 7i

• 1 - 3i

• 1 - 7i

• 7 - 3i

Multiple Choice

(4 - 2i) - (3 + 6i)

• 7 - 4i

• 1 + 4i

• 1 - 8i

• 7 - 8i

Multiple Choice

(3 + 8i)(-2 - i)

• 2-19i

• 23-i

• 34+5i

• 23-i

Multiple Choice

(3i)(-2+4i)

• -6+12i

• -12-6i

• -2+7i

• 12+6i

Multiple Choice

Simplify

• (-10+6i)/17

• (1+50i)/61

• (-23+36i)/25

• (-21+33i)/34

Multiple Choice

(-7 + 9i) + (2 - 10i)

• -5 + i

• -5 - i

• -9 + 1

• 9 - i

Multiple Choice

What is the conjugate of -2+5i ?

• -5 + 2i

• -2 - 5i

• 2 + 5i

• 5 - 2i

Multiple Choice

• 5i

• -5i

• 5+i

• -5

Multiple Choice

What is the complex conjugate of  4-3i ?

• 1/(4-3i)

• 1/(4+3i)

• -4 + 3i

• 4 + 3i

Multiple Choice

Simplify
(-6 - 2i)²

• 32

• 36-4i

• 36+24i

• 32+24i

Fill in the Blank

$$-4i\cdot5i$$  

Multiple Choice

Which is the complex conjugate of $$\left(-4i+3\right)$$  ?

• $$\left(3-4i\right)$$  

• $$\left(3+4i\right)$$  

• $$\left(-3-4i\right)$$  

• $$-i$$  

Multiple Choice

Where is point B located?

• 2 + i

• -3

• 2i

• -1 - i

Multiple Choice

Where is point C located?

• 2 + i

• -3

• 2i

• -1 - i

Multiple Choice

Where is point A located?

• 2 + i

• -3

• 2i

• -1 - i

Multiple Choice

What complex number is represented by the graph?

• -3-i

• -3+i

• 1+3i

• 1-3i

Multiple Choice

What are the zeroes of the graph?

• x = {-3, 1}

• x = {-3}

• x = {-8, 1}

• x = {-4, -2}

Multiple Choice

Determine the solution(s) to the quadratic equation:

$$x^2+6x=-9$$  

• x = {6}

• x = {-9}

• x = {3}

• x = {-3}

Multiple Choice

Determine the solution(s) to the quadratic equation:

$$x^2-81=0$$  

• x = {9}

• x = {-9}

• x = {-9, 9}

• No solution

Multiple Choice

Determine the solution(s) to the quadratic equation:

$$x^2-10x-24=0$$  

• x = {-24, -10}

• x = {10, 24}

• x = {-12, 2}

• x = {-2, 12}

Multiple Select

Classify

$$\frac{3}{5}$$  

• Irrational

• Rational

• Integer

• Whole

• Natural

Multiple Select

Classify

$$\pi$$  

• Irrational

• Rational

• Integer

• Whole

• Natural

Multiple Select

Classify:

-0.54

• Irrational

• Rational

• Integer

• Whole

• Natural

Multiple Select

Classify:

0

• Irrational

• Rational

• Integer

• Whole

• Natural

Multiple Select

Classify:

-9

• Irrational

• Rational

• Integer

• Whole

• Natural

Multiple Select

Classify:

$$2i$$  

• Irrational

• Complex

• Integer

• Pure Imaginary

• Real

Multiple Select

Classify:

$$-2+9.3i$$  

• Irrational

• Complex

• Integer

• Pure Imaginary

• Real

Multiple Choice

A parabola has a vertex at (-3,2).
Where is the axis of symmetry?

• y = -2

• x = 3

• x = -3

• y = 2

Multiple Choice

Convert the equation y = x²-2x-5 into vertex form. 

• y= (x-1)²-6

• y= -(x-1)²-6

• y= (x+1)²-6

• y= -(x+6)²-1

Multiple Choice

$$y=4(x+2)^2-8$$ Convert the equation from vertex form to standard form. 

• $$y=4x^2+16x+8$$  

• $$y=4x^2+16x+16$$  

• $$y=16x^2+64x-8$$  

• $$y=16x^2+256x+8$$  

Multiple Choice

Write the following quadratic expression in vertex form:

x² + 4x + 10

• (x + 4)² + 6

• (x + 2)² + 6

• (x + 4)² - 6

• (x + 2)² - 6

Multiple Choice

What is another word for ROOTS?

• Zeros

• y-intercept

• Maximum

• Vertex

Multiple Choice

What is the vertex of this function?

• (-3, -4)

• (-4, -3)

• (0, 5)

• (-5, 0)

Multiple Choice

Which of the following is the correct equation for the given graph?

• f(x) = (x - 2)² - 1

• f(x) = (x + 2)² - 1

• f(x) = -(x + 2)² - 1

• f(x) = -(x - 2)² - 1

Multiple Choice

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5, -4)

• (-5, -4)

• (-15, -4)

• (15, -4)

Multiple Choice

How many solutions are there?

• 2 imaginary

• 1 repeated real

• 2 real

• 0

Multiple Choice

Solve using the quadratic formula. $$f\left(x\right)=2x^2-4x+7$$  

• $$\frac{2\pm2i\sqrt{10}}{2}$$  

• $$\frac{4\pm\sqrt{40}}{4}$$  

• $$\frac{2\pm i\sqrt{10}}{2}$$  

• $$\frac{2\pm2i\sqrt{40}}{4}$$  

Multiple Choice

Solve using the quadratic formula.
2x² - 9x - 35 = 0

• x = 7/2, x = -6

• x = -5/2, x =5

• x = -3/7, x =6

• x = -5/2, x = 7

Multiple Choice

Solve: $$11x^2-4x+11=0$$  

• $$\frac{2\pm3i\ \sqrt[]{13}}{11}$$  

• $$\frac{13}{11}\ and\ \frac{-9}{11}$$  

• $$\frac{4\pm3i\ \sqrt[]{13}}{22}$$  

• $$\frac{2\pm3\sqrt[]{13}}{11}$$  

Multiple Choice

$$8x^2+12x+9=0$$  

• $$\frac{-3\pm3i}{4}$$  

• $$0\ and\ \frac{3}{2}$$  

• $$\frac{-3\pm12i}{4}$$  

• $$\frac{-3\pm3\sqrt[]{3}}{4}$$  

Multiple Choice

$$x^2-6x+4=0$$  

• $$3\pm\sqrt{5}$$  

• $$\frac{6\pm\sqrt{20}}{2}$$  

• $$3\pm\sqrt{20}$$  

• $$3\pm i\sqrt{13}$$  

Multiple Choice

Look at the equation below.

$$x^2+2x-5=2$$  

Which values of x satisfy the equation? Write your answers in simplest radical form.

• $$-1\pm2\sqrt{2}$$  

• $$1\pm2\sqrt{2}$$  

• $$-1\pm2i\sqrt{2}$$  

• $$1\pm2i\sqrt{2}$$  

Multiple Choice

The discriminant is

• aX²  + bX  +  c

• b - 4ac

• b² - 4ac

• b² + 4ac

Multiple Choice

What is the discriminant of -2x² − x − 1 = 0

• 76

• -7

• 9

• none of these

Multiple Choice

If the discriminant is positive, then the solution will be

• one real solution

• two real solutions

• no real solutions

• one imaginary solution

Multiple Choice

A function has a discriminant of 25.
______________
How many solutions does it have?

• 0

• 1

• 2

• 5

Multiple Choice

A function has a discriminant of -3.
______________
How many x-intercepts does it have?

• 0

• 1

• 2

• 3

Multiple Choice

____________
For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

• Not Sure

Multiple Choice

____________
For the function above, is the discriminant positive, negative, or zero?

• Positive

• Negative

• Zero

• Not Sure

Multiple Choice

What is the discriminant and how many solutions would this quadratic have?

-4x² - 8x - 8 = -4

• 0, No Solutions

• 0, 1 Solution

• 128, 2 Solutions

• 128, 1 Solution

Multiple Choice

What is the domain of the function?

• x ≥ 3

• x ≤ 3

• All real numbers

• -1 ≤ x ≤ 5

Multiple Choice

What is the range of the function?

• x ≥ 3

• x ≤ 3

• All real numbers

• -1 ≤ x ≤ 5

Multiple Choice

What is the max/min value?

• Minimum of 3

• Minimum of -2

• Maximum of 0

• Maximum of 7