# Algebra 2 Unit 4 Flashcards

1
Q

Graphically, what are the solutions to a quadratic equation?

A

The points at which the function intersects the x-axis

2
Q

How many possible solutions are there in a quadratic equation?

A

2, 1, or 0

3
Q

When are the two solutions in a quadratic equation?

A

When the A and C values of the equation have opposite signs

4
Q

When is there one solution in a quadratic equation?

A

When the vertex falls on the x-axis

5
Q

When are there no solutions in a quadratic equation?

A

When the A and C values of the equation have the same signs

6
Q

When factoring, what do you always look for first?

A

The GCF or Greatest Common Factor

7
Q

What is the GCF of 12k - 18

A

6

8
Q

What is the GCF of 9x - 24x

A

3x

9
Q

What is the opposite of Factoring?

A

FOIL

10
Q

What is the opposite of FOIL?

A

Factoring

11
Q

When factoring a quadratic and a>1, what trick should you remember?

A

To divide by A and apply the reduce and slide method

12
Q

What is the difference of squares?

A

a^2 - b^2 = (a - b) (a+ b)

13
Q

What are the three steps to solve quadratics by factoring?

A
1. Move all terms to one side and set to zero. 2. Factor 3. Set each factor to 0 and solve each
14
Q

The imaginary letter i is also know as …

A

The square root of negative one

15
Q

The square root of negative one is also known as …

A

The imaginary letter i

16
Q

The swuare root of negative nine is …

A

3i

17
Q

i squared is equal to …

A

Negative One

18
Q

i to the 3rd power is …

A

Negative i

19
Q

i to the 4th power is …

A

1

20
Q

When dealing with negative square roors, what is the first step?

A

Take out the imaginary i

21
Q

What is the standard form of a complex number?

A

a + bi

22
Q

In a + bi, what is a?

A

The real part

23
Q

In a + bi, what is bi?

A

The imaginary part

24
Q

What must the conditions be when completing the square?

A

The a value must be 1 and the b value must be even

25
Q

What must the conditions be when solving by square roots?

A

There must be no b term in the given quadratic equation

26
Q

When can you use the quadratic formula?

A

Always, it never fails

27
Q

What must the conditions be when solving by factoring?

A

The roots must be rational

28
Q

What is the discriminant?

A

b^2 - 4ac (The Randicand in the quadratic formula)

29
Q

How many roots and what type when the discrimnant is a perfect square and greater than 0?

A

2 real rational roots

30
Q

How many roots and what type when the discrimnant is a not perfect square and greater than 0?

A

2 real irrational roots

31
Q

How many roots and what type when the discrimnant is equal to 0?

A

1 real rational root

32
Q

How many roots and what type when the discrimnant is less than 0?

A

2 imaginary roots

33
Q

When d = 64, what type and how many roots do you have?

A

2 real rational roots

34
Q

When d = 32, what type and how many roots do you have?

A

2 real irrational roots

35
Q

When d = 0, what type and how many roots do you have?

A

1 real rational root

36
Q

When d = -4, what type and how many roots do you have?

A

2 imaginary roots

37
Q