1.5 Quadratic Equations Flashcards
a polynomial where the highest exponent is 2 (2nd degree)
quadratic
standard form for a quadratic equation
What are the 4 ways to solve a quadratic equation
Factoring
Square Root Property
Completing the Square
Quadratic Formula
When using the square root property, what must you remember?
Isolate the squared term before taking the square root of both sides of the equation.
When using factoring to solve a quadratic equation, what must you remember to do?
Set one side = 0 before factoring.
When you take the square root of both sides of an equation, how many answers should you get?
2 unless you are taking the square root of 0. If you are taking the square root of 0, you will only get one answer.
Describe the process of completing the square.
1) Make sure the coefficient of the squared term is equal to 1. If it is not, divide every term by this number.
2) Take the constant term to the right side of the equation.
3) Set up your blanks.
4) Take the “x” term and divide by 2.
5) Square x/2.
6) Place this answer on both sides of the equation in the blanks.
7) Factor the left side (trinomial perfect square).
8) Take the square root of both sides.
9) Solve for x.
10) There should be two answers unless you are taking the square root of 0. Then you have one answer.
What is the quadratic formula?
What does a discriminant tell you?
the type of solutions you will get when solving a quadratic equation
What is the formula for the discriminant?
If the discriminant is equal to 0, how many and what type of solutions do you have?
1 real solution
If the discriminant is equal greater than 0, how many and what type of solutions do you have?
2 real solutions
If the discriminant is less than 0, how many and what type of solutions do you have?
2 imaginary solutions
