Chapter 5 (Alg 2) Flashcards
Quadratic Function
a function that can be written in the standard form y = ax^2 + bx + c were a DNE 0
Parabola
Graph of a Quadratic formula
Axis of Symmetry
divides the Parabola into mirror images and passes through the vertex
Vertex
The lowest or highest point on a parabola
Graphing a standard quadratic function
Draw axis of symmetry, x = -b/2a
Plot the vertex
Fill in some data values
Monomial
a number, a variable, or the product of a number and one or more variables with whole number exponents
Bi-nomial, Tri-, Poly-
the sum of two monomials, three, four or more
Vertex form of Quadratic
y = a(x-h)^2 + k, h is the axis of symmetry (this is standard for a lot of the equations you’ll come across in the future)
Graphing Vertex form of Quadratic
Draw axis of symmetry, plot vertex (h,k), plot more data points
Intercept form of Quadratic
y = (x - p) (x - q)
How to graph intercept form of Quadratic
Draw axis of symmetry which is p + q over 2, Plot vertex, plot more data points
Minimum and Maximum of Quadratic graph
a > 0, the y-coordinate of the vertex
a
How to factor a Trinomial
find integers m and n such that m + n = b and mn = c
(x^2 + bx + c)
Quadratic equation
written as ax^2 + bx + c = 0
Zero product property
Let A and B be expressions, if AB = 0, then A = 0 or B = 0
Factor a trinomial ax^2 +…
finding numbers k and j whose product is a and numbers mn = c
Zeros of a function
x-values for which the function’s value is zero, there also the x-intercepts.
Differences of Two Squares Pattern
a^2 - b^2 = (a+b)(a-b)
Perfect Square trinomial patterns
a^2 + 2ab + b^2 = (a + b)^2
a^2 - 2ab + b^2 = (a - b)^2
Square root (definition)
If b^2 = a then Sqrt. a = b
A number b is a square root of a number a if b^2 = a
A positive number a has two square roots written Sqrt.a and - Sqrt. a
Radical
the expression Sqrt. a
Radical Sign
Sqrt. sign (not technically)
Radicand
the expression under the Radical
Properties of Square Roots (Product, Quotient)
Sqrt. ab = Sqrt. a times Sqrt. b
Sqrt. (a over b) = Sqrt. a over Sqrt. b
Imaginary unit i
Defined as a number such that i^2 equals -1, i = Sqrt. -1
Complex number
(a + bi), a is the real part, bi is the imaginary part
{}
To add or subtract complex numbers, add or subtract their real and their imaginary parts separately
Complex Conjugates
in the form of a + bi and a - bi, Using the special product rule, multiplying them will result in all real numbers
Completing the square
adding a constant c to the expression x^2 + bx to make it a perfect square trinomial
{}
x^2 + bx + (b/2)^2 = (x + b/2)^2
Quadratic Formuala
x = (-b + - Sqrt. b^2 -4ac)/ 2a
If the Discriminent is >, =,
2 real solutions
1 real solution
2 imaginary solutions
Vertical Motion Models (Dropped, falling object; Launched or Thrown Object)
h = -16t^2 + h sub 0 h = -16t^2 + v sub 0 t + h sub 0
Rationalizing the denominator
Eliminating any radical from the denominator, to simplify
The Square root of a negative number
If r is a positive real number, then Sqrt. -r = iSqrt.r By property (1), it follows that (iSqrt.r)^2 = -r
