Algebra 2 Unit 4 Flashcards
Graphically, what are the solutions to a quadratic equation?
The points at which the function intersects the x-axis
How many possible solutions are there in a quadratic equation?
2, 1, or 0
When are the two solutions in a quadratic equation?
When the A and C values of the equation have opposite signs
When is there one solution in a quadratic equation?
When the vertex falls on the x-axis
When are there no solutions in a quadratic equation?
When the A and C values of the equation have the same signs
When factoring, what do you always look for first?
The GCF or Greatest Common Factor
What is the GCF of 12k - 18
6
What is the GCF of 9x - 24x
3x
What is the opposite of Factoring?
FOIL
What is the opposite of FOIL?
Factoring
When factoring a quadratic and a>1, what trick should you remember?
To divide by A and apply the reduce and slide method
What is the difference of squares?
a^2 - b^2 = (a - b) (a+ b)
What are the three steps to solve quadratics by factoring?
- Move all terms to one side and set to zero. 2. Factor 3. Set each factor to 0 and solve each
The imaginary letter i is also know as …
The square root of negative one
The square root of negative one is also known as …
The imaginary letter i
The swuare root of negative nine is …
3i
i squared is equal to …
Negative One
i to the 3rd power is …
Negative i
i to the 4th power is …
1
When dealing with negative square roors, what is the first step?
Take out the imaginary i
What is the standard form of a complex number?
a + bi
In a + bi, what is a?
The real part
In a + bi, what is bi?
The imaginary part
What must the conditions be when completing the square?
The a value must be 1 and the b value must be even
What must the conditions be when solving by square roots?
There must be no b term in the given quadratic equation
When can you use the quadratic formula?
Always, it never fails
What must the conditions be when solving by factoring?
The roots must be rational
What is the discriminant?
b^2 - 4ac (The Randicand in the quadratic formula)
How many roots and what type when the discrimnant is a perfect square and greater than 0?
2 real rational roots
How many roots and what type when the discrimnant is a not perfect square and greater than 0?
2 real irrational roots
How many roots and what type when the discrimnant is equal to 0?
1 real rational root
How many roots and what type when the discrimnant is less than 0?
2 imaginary roots
When d = 64, what type and how many roots do you have?
2 real rational roots
When d = 32, what type and how many roots do you have?
2 real irrational roots
When d = 0, what type and how many roots do you have?
1 real rational root
When d = -4, what type and how many roots do you have?
2 imaginary roots
What is the quadratic formula?
