15 functions - 16 quadratics

Question 1

define

a function is like a

Answer 1

a machine that takes an input, transforms it, and spits out an output

Question 2

example

in f(x) = x^2 + 1

Answer 2

every input (x) is squared and added to one to get the output f(x)

Question 3

define

because a fraction can’t be divided by 0, when the denominator is zero, a function is

Answer 3

undefined

Question 4

define

Domain is

Answer 4

the set of all possible input values (x) to a function (values that don’t lead to an invalid operation or an undefined output)

Question 5

define

Range

Answer 5

the set of all possible output values (y) from a function

Question 6

define

what are vertical asymptotes?

Answer 6

a vertical line that guides the graph of the function but is not part of it

Question 7

define

what are horizontal asymptotes?

Answer 7

a horizontal line that is not part of a graph of a function but guides it for x-values

Question 8

technique: functions

to find the domain, start with

Answer 8

all real numbers and exclude the values of x for which the function is invalid or undefined

Question 9

technique: functions

to find the range,

Answer 9

graph the function on your calculator and figure out the possible values of y, taking note of any horizontal asymptotes

Question 10

technique: functions

anytime f(x) is used in a graphing question,

Answer 10

think of it as the y

Question 11

define

what is a point?

Answer 11

an input and an output, an x and a y

Question 12

confusing concept

zeros, roots, and x intercepts of a function are all

Answer 12

different terms for x that makes f(x) = 0

Question 13

define

a constant is a

Answer 13

function
no matter the input, the same output always results

Question 14

confusing concept

solutions to f(x) = k refers to

Answer 14

the intersection points of f(x) and the horizontal line y = k

Question 15

confusing concept

consider constants as ___________ lines

Answer 15

horizontal lines
e.g. f(x) > 5 means the entire graph of f is above the horizontal line y=5

Question 16

define

f(x) = ax^2 + bx + c

Answer 16

a quadratic in the form of a function

Question 17

define

the roots/x intercepts/solutions refer to the

Answer 17

values of x that make f(x) = 0

Question 18

key formula

sum of the roots

Answer 18

-b/a
in quadratic ax^2 + bx + c

Question 19

key formula

product of the roots

Answer 19

c/a

Question 20

define

vertex is

Answer 20

the midpoint of the parabola

Question 21

confusing concept

the x coordinate of the vertex is always

Answer 21

the midpoint of the two roots

Question 22

confusing concept

vertex form is one way of

Answer 22

representing a quadratic function

Question 23

key formula

vertex form equation

Answer 23

y = a(x-h)^2 + k

Question 24

technique: functions (vertex form)

to get a quadratic function into vertex form,

Answer 24

must complete the square

Question 25

example

complete the square of
y = x^2 - 4x - 21

Answer 25

A. b = b/2
-4 = -4/2 = -2
=> y = (x-2)^2 - 21
B. (-2)^2 = 4
=> y = (x-2)^2 - 21 - 4
= y = (x-2)^2 - 25
C. vertex = (2, -25)

Question 26

technique

vertex form allows

Answer 26

to find the vertex without knowing the roots of a quadratic

Question 27

formula

discriminant is equal to

Answer 27

b^2 - 4ac

Question 28

confusing concept

the sign of the discriminant indicates

Answer 28

how many solutions there are for a parabola

Question 29

technique

if D > 0,

Answer 29

there are two real roots (two solutions)

Question 30

technique

if D = 0,

Answer 30

there is one real root

Question 31

technique

if D < 0,

Answer 31

there are no real roots

Question 32

key formula

quadratic formula

Answer 32

x = (-b±√(b²-4ac))/(2a)

Question 33

explanation

when b²-4ac > 0

Answer 33

the “±” in the quadratic formal takes effect and results in two different roots

Question 34

explanation

when b²-4ac = 0, what is its effect in the quadratic formula

Answer 34

since the “b²-4ac” part in the quadratic formal equal to zero, we’re essentially adding and subtracting 0, both of which gives the same root; hence, one real root/solution/x intercept

Question 35

explanation

when b²-4ac < 0

Answer 35

we’re taking the square root of a negative number, which is undefined and gives us no real roots

Question 36

technique

when asked for the maximum or the minimum of a quadratic,

Answer 36

find the vertex

Question 37

define

what is an asymptote?

Answer 37

An asymptote is a line that is never crossed by the function

Question 38

technique

where do you find the vertical asymptote?

Answer 38

vertical asymptotes are found where the bottom of the fraction is zero (because you are never allowed to divide by zero)

Question 39

confusing concept

even if a quadratic doesn’t have any real roots,

Answer 39

it can have imaginary roots