Algebra 2 - Quadratic Equations
Factor and solve by using the Zero Product Property. x2 + 8x + 16=0
(x+4)(x+4)=0 x+4=0 or x+4=0 x=-4
Factor and solve by using the Zero Product Property. x² - 4x - 21=0
(x-7)(x+3)=0 x-7=0 or x+3=0 x=7 or x=-3
What is a parabola?
A curved graph of a quadratic function.
x² - y² = (x + y)(x - y) is an example of what?
A difference of two square
x²- 4x + 4 is an example of what?
A perfect square trinomial
What is a domain?
A set of all x values in a function.
What is a range?
A set of all y values in a function.
What is an axis of symmetry?
A vertical line that divides the parabola into two congruent halves.
What is a monomial?
An expression with just one term. Example: 3x²
What is a polynomial?
An expression with more than three terms. Example: x⁴-2x³+5x²+x-1
What is a trinomial?
An expression with three terms. Example: 3x² − 4x + 2
What is binomial?
An expression with two terms. Example: 3x² + 2
What is the standard form of a quadratic equation?
An expression written in order from highest exponent to the lowest. y = ax²+bx+c Example: x²+8x+12 Non-example: x-4+3x+x4
Factor the following problem: x²+8x+12
Answer: (x+2)(x+6)
What is the fourth step when factoring a trinomial?
Check by multiplying both binomials.
What is the first step when factoring a trinomial?
Create a binomial skeleton containing the correct signs of the bx and c terms. Example: ( + )( + )
What is the third step when factoring a trinomial?
Drop factors into the skeleton.
True or False? Is this written in standard form? 6=7x−x²
False. The problem in standard form would be -x²+7x−6
True or False? Is this written in standard form? 3x+x²+12
False. The problem in standard form would be x²+3x+12
What is the second step when factoring a trinomial?
Identify factors of the constant. Add all factors to see which will equal the bx term.
What is the BOX method?
Multiplying two binomial answers of a trinomial expression to check that the answers are correct by using a 2x2 square.
What is the FOIL method?
Multiplying two binomial answers of a trinomial expression to check that the answers are correct. FOIL stands for First, Outer, Inner, Last
What is the zero product property?
Set both factors to equal zero and solve.. Example: If x × y = 0 then x = 0 or y = 0 (or both x = 0 and y = 0)
What are some real world examples of Quadratic Parabolas?
The Saint Louis Arch The Golden Arches of McDonald's The base of Eiffel Tower
What is a leading coefficient?
The first number in a line of coefficients and variables. The expression must be in standard form. Example: 7 is the leading coefficient in the expression 7x³-2x²+2x-4
What is a coefficient?
The number multiplied by a variable. Example: 5 is the coefficient in 5x
Factoring
The process of breaking a number down into its factors. Example: All the factors of the number 12 2 × 6 = 12, but also 3 × 4 = 12, and of course 1 × 12 = 12. So 1, 2, 3, 4, 6 and 12 are factors of 12. And also -1,-2,-3,-4,-6 and -12, because you get a positive number when you multiply two negatives, such as (-2)×(-6) = 12 Answer: 1, 2, 3, 4, 6, 12, -1, -2, -3, -4, -6, -12
Define perfect square trinomials.
The product you get when you multiply a binomial by itself twice. Example: (x-2)(x-2) = x²- 4x + 4
What is a vertex?
The turning point of the graph of a function. It may be a maximum or a minimum.
True or False? Is this written in standard form? 4x²+3x+2
True.
True or false: x² = x¹*x¹
True. When multiplying like variables with exponents all you have to do is add the exponents. Example: 5x²*x= 5x³
Define difference of two squares.
Two terms that are squared and separated by a subtraction sign and can be factored into (x+y)(x−y). Example: x²-4 = (x+2)(x-2)
What is the Quadratic Function?
f(x) = x² Example: If x = -2 then f(x) = (-2)² so f(x) = 4 this will give you your coordinates for your point to graph which is (-2,4)