C6 (Graphs)

Question 1

which way up is a parabola

Answer 1

positive parabola = smiley face
negative parabola = sad face

Question 2

flipping a parabola

Answer 2

smmiley -> sad
same roots (where x = 0)
inverse y coords (so inverse t.p.)

Question 3

explain y = mx + c

Answer 3

straight line with gradient m, crosses y-axis at (0,c)

Question 4

graph y = sinx
(max, min, where does it cross, symmetries)

Answer 4

symmetry:
from 90 to 180 curve is a reflection of the first part in the line x = 90
from 180 to 360 there is a rotation of the previous 180 part through 180 with centre (180,0)

Question 5

graph y = cosx
(max, min, where does it cross)

Answer 5

basically sinx shift 90 degrees left
reflective symmetry about the axis

Question 6

graph y = tanx
(where does it cross, what else)

Answer 6

crosses where sinx = 0
asymptotes where cosx = 0 (where value is undefined)

because tan = sin/cos

Question 7

graph of y = 2^x and y = 2^-x

Answer 7

reflections of each other in the y-axis

Question 8

y = 2sinx

Answer 8

Question 9

y = sin2x

Answer 9

Question 10

how to reflect a graph in y-axis

Answer 10

turn x into -x

Question 11

how to ‘use symmetries’ to solve sinx/cosx/tanx = y

Answer 11

on calculator find reference angle α by doing sin/cos/tan^-1(y)

using α:
(sin) x = 180 - α
(cos) x = 360 - α
(tan) x = a + 180

Question 12

what is formula of this graph

Answer 12

y=(x-1)(x+2)(x+3)(x-5)

Question 13

Answer 13

horizontal shift +1 / -1

Question 14

Answer 14

vertical shift up 1