Vocab and Concepts - Quadratic Functions and Equations Flashcards
What is the definition of i?
√-1
What is determined in a function when y=0?
x- intercepts
What is determined in a function when x=0?
y-intercepts
What is standard form of a quadratic function?
y= ax² + bx + c
What is vertex form of a quadratic function
y= a(x-h)² + k
What must one use first when given the standard form of the quadratic function?
x= -b/2a
What is the difference between instructions to factor or factor completely and instructions to solve?
A factoring problem does not have an equal sign.
When a graph is translated to the left, the number of spaces should be ______ from x.
Subtracted
When a graph is translated to the right, the number of spaces should be ______ from x.
Added
What method of factoring should always be attempted first?
Common monomial
What method is used if an expression will not factor?
Quadratic formula
What is the quadratic formula?
x= -b±√b²-4ac/2a
The “k” or y-coordinate of the vertex is always equal to the ______ or ______ of a function.
Maximum or minimum
How can we obtain a quadratic regression given a table of values?
Stat→ edit→L₁ , L₂ → stat→calc→5→ enter
To find a minimum or maximum, one must simply find the _____.
Vertex
Explain how to rationalize a complex number.
Take the conjugate of the denominator and use FOIL (sometimes distributive) to multiply it by both the numerator and denominator.
What are the four things we find when we set a quadratic equal to zero and solve?
- Zeros
- Solutions
- X-intercepts
- Roots
When we are given a vertex (h,k) and a point (x,y) to find an equation of a parabola, what is the value we have left to find?
a
What is the discriminant and what does it tell us?
b²-4ac - It tells us the number and kind of solutions.
b²-4ac > 0, 2 real
b²-4ac = 0, 1 real
b²-4ac < 0, 2 imaginary
Show an example of a factor pair and factor it.
a² - 5a -14= (a-5) (a+7)
Show an example of a difference of squares and factor it.
16x² - 2y²
(4x)² - (5y)²
(4x-5y) (4x+5y)
Show an example of trial and error and factor it.
2x² +11x +12 2x² +8x+3x+12 (2x²+8x) (3x+12) 2x(x+4) +3(x+4) (x+4) (2x+3)
