Chap 18 - Quadratic, cubic, exponential, reciprocal graphs, differentiation

Question 1

vids:
https://www.youtube.com/watch?v=ia51_eXDAQ0
https://www.youtube.com/watch?v=fV6zQwIMUx8
https://www.youtube.com/watch?v=wCA1VskgTag
https://www.youtube.com/watch?v=1xmdZ2Wqznc

Question 2

what do you call the line in
1)quadratic
2) reciporical

Answer 2

1) Parabola
2) hyperbola

Question 3

Types of graphs

Answer 3

-linear
-Quadratic
-Cubic
-Quartic
-Exponential
-Reciprocal

Question 4

shapes of ( + ) & ( - ) graphs

Answer 4

positive & negative
linear: / \
quadratic: U ∩
Cubic: up & down, down & up
Quartic: M W
exponential: down to up, up to down
reciprocal: |_ _|
-| |-

Question 5

how many turning point does each graph have

Answer 5

-linear - 0
-Quadratic - 1
-Cubic - 2
-Quartic - 3

Question 6

formula for exponential graph = formula for compound interest

Answer 6

P = principle
R = rate from % in DECIMALS
t = time
A = total amount
P (1 +/ - R)^ t = A
-appreciation/ growth = ( + )
-depreciation/ decay = ( - )
*total money including compound interest

Question 7

what makes the graph like that

Answer 7

-linear - x power = 1
-Quadratic - x power = 2
-Cubic - x power = 3
-Quartic - x power = 4
-Exponential - x = power of number
-Reciprocal = x = denominator

Question 8

what do reciprocal graphs have

Answer 8

-asymptote = point where line goes to infinity = never touches x axis because denominator = 0, not always x = 0
-so there’s a gap in the middle
-so don’t have to find when x = 0 when doing table of values
-lines can touch the y axis depending on the y intercept which either brings the graph up or down

Question 9

steps to graphing

Answer 9

-predict shape
-substitute values/ table of values
-plot & draw

Question 10

note: in calc put negative no. in ( )

Question 11

relationship btw numerator & lines in reciprocal graph

Answer 11

1) numerator> 1:
-lines move more outward from the center
2) 0< numerator< 1:
-lines move more inwards to center
3) numerator = ( - ):
-quadrants will swap

Question 12

how to draw quadratic graph

Answer 12

1)find x & y intercepts
-make x or y = 0 & find the other coordinate
2)find coordinates of turning point
-x = -b/ 2a
*substitute x to find coordinate of y
(axis of symmetry - x = _____)
-derive equation & make it = 0

Question 13

how to find turning point for quadratic equation

Answer 13

1)derive the equation & make it = 0 (because turning point gradient = 0)
2) uses formula
-x = -b/ 2a
-substitute x to find coordinate of y
(axis of symmetry - x = _____)
* get x then substitute in to find y

Question 14

formula for Turning point x coordinate (only used for Quadratic)

Answer 14

x = -b
———
2a

Question 15

ways to find x intercept

Answer 15

-ALWAYS TRY TO TAKE OUT COMMON FACOTRS FIRST
-Quadratic formula: works only when there is x intercept at y)
-completing squares: works when a = 1
-taking out common factor: work when there’s common factors
-trick: a > 1

Question 16

how to find quadratic equation from graph

Answer 16

-find x intercept
-put in factorizing format: (x +/- ____) (x +/- ____)
-each bracket has to = 0

Question 17

format for equations:
-linear
-Quadratic
-Exponential
-Reciprocal

Answer 17

y = mx + c
y = ax^2 + bx + c
y = a^x
y = a/ x

Question 18

Quadratic formula

Answer 18

         2a -put bracket in calc when (b)^2

Question 19

how to complete squares to factories

Answer 19

• b / 2
• ( x +/- b/2 )^2 = make it into a perfect square
• ( + )/ ( - ) no. to make perfect square to match with equation
  -check if it matched by expanding

Question 20

how to use trick to factories when a> 1 (linear)

Answer 20

-multiple c by a
-remove a from equation
-fractorise equation normally
-divide no.s by a only, not x
-simplify fractions
-multiple x by denominator of fraction for each bracket
-expand to check

Question 21

how many point of interaction can a liner & quadratic graph have

Answer 21

0, 1, 2
usually 2, so get 2 coordinates for ans

Question 22

note: you can graph only linear & quadratic algebraically, use table of values for others

Question 23

ways to find gradient of curve

Answer 23

-tangent at a point
-differentiate

Question 24

how to find gradient of a curve at a tangent

Answer 24

-draw a tangent at a point
-find gradient of that tangent

Question 25

how to find gradient of a curve using derivitives

Answer 25

-dy/ dx = gradient equation
-subtitle values of x from a point to find gradient

Question 26

gradient at turning point

Answer 26

0

Question 27

rules for differientiation

Answer 27

-multiply coefficient of x with power, minus power by 1
-if power = 0, take only coefficient if there is or just 1
-if number without x, remove it

Question 28

how to find turning point

Answer 28

-derived equation
-make derived equation = 0 to find x coordinate
-subtitle x coordinate to find y coordinate
because gradient of turning point = 0

Question 29

how to find equation of tangent

Answer 29

-find point that the tangent touches
-gradient of that point
-find equation of tangent using y - y1 = m (x - x1) using coordinates of that point

Question 30

how to find local max & min turning point for quadratic & cubic

Answer 30

-draw the rough shape of the graph
-local max = highest turning point
-local min = lowest turning point

Question 31

formula for y-intercept/ equation of straight line

Answer 31

-need 1 point & gradient
y - y1 = m (x - x1)

Question 32

note: square rooting has a positive & negative value